Mountain o' Mounts

Darnassus exalted - 6 Mounts

* 1 - Reins of the Swift Frostsaber 100G
2 - Reins of the Swift Mistsaber 100G
3 - Reins of the Swift Stormsaber 100G
4 - Reins of the Spotted Frostsaber 10G
5 - Reins of the Striped Frostsaber 10G
6 - Reins of the Striped Nightsaber 10G

Ironforge exalted - 6 Mounts

* 7 - Swift Brown Ram 100G
8 - Swift Gray Ram 100G
9 - Swift White Ram 100G
10 - Brown Ram 10G
11 - Gray Ram 10G
12 - White ram 10G

Stormwind exalted - 7 Mounts

* 13 - Swift Brown Steed 100G
14 - Swift Palomino 100G
15 - Swift White Steed 100G
16 - Brown Horse Bridle 10G
17 - Chestnut Mare Bridle 10G
18 - Pinto Bridle 10G
19 - Black Stallion Bridle 10G

Exodar exalted - 6 Mounts

* 20 - Great Blue Elekk 100G
21 - Great Green Elekk 100G
22 - Great Purple Elekk 100G
23 - Brown Elekk 10G
24 - Gray Elekk 10G
26 - Purple Elekk 10G

Gnomeregan Exiles exalted - 7 Mounts

* 26 - Swift Green Mechanostrider 100G
27 - Swift White Mechanostrider 100G
28 - Swift Yellow Mechanostrider 100G
29 - Blue Mechanostrider 10G
30 - Green Mechanostrider 10G
31 - Red Mechanostrider 10G
32 - Unpainted Mechanostrider 10G

Wintersaber Trainers exalted - 1 Mount

* 33 - Reins of the Winterspring Frostsaber 100G

Kurenai exalted - 8 Mounts

* 34 - Reins of the Cobalt War Talbuk 100G
35 - Reins of the Cobalt Riding Talbuk 70G
36 - Reins of the Silver War Talbuk 100G
37 - Reins of the Silver Riding Talbuk 70G
38 - Reins of the Tan Riding Talbuk 70G
39 - Reins of the Tan War Talbuk 100G
40 - Reins of the White Riding Talbuk 70G
41 - Reins of the White War Talbuk 100G

Sha'tari Skyguard exalted - 5 Mounts

* 42 - Blue Riding Nether Ray 200G
43 - Green Riding Nether Ray 200G
44 - Purple Riding Nether Ray 200G
45 - Red Riding Nether Ray 200G
46 - Silver Riding Nether Ray 200G

Netherwing exalted - 6 Mounts

* 47 - Reins of the Azure Netherwing Drake 200G
48 - Reins of the Cobalt Netherwing Drake 200G
49 - Reins of the Onyx Netherwing Drake 200G
50 - Reins of the Purple Netherwing Drake 200G
51 - Reins of the Veridian Netherwing Drake 200G
52 - Reins of the Violet Netherwing Drake 200G

Grypon venor in Shadowmoon Valley - 7 Mounts

* 53 - Swift Blue Gryphon 200G
54 - Swift Green Gryphon 200G
55 - Swift Purple Gryphonnn Flamebeard 200G
56 - Swift Red Gryphon 200G
57 - Ebon Gryphon 100G
58 - Golden Gryphon 100G
59 - Snowy Gryphon 100G

Cenarion Expedition exalted - 1 Mount

* 60 - Cenarion War Hippogryph 1600G

The Sons of Hodir revered - 1 Mount, exalted - 1 Mount

* 61 - Reins of the Ice Mammoth 800G
62 - Reins of the Grand Ice Mammoth 8000G

Wyrmrest Accord exalted - 4 Mount

* 63 - Reins of the Red Drake 1600G

Mei Francis (neutral Kirin Tor faction) - 4 Mounts

* 64 - Armored Snowy Gryphon 2000G
65 - Reins of the Armored Brown Bear 750G
66 - Reins of the Traveler's Tundra Mammoth 20000G
67 - Reins of the Wooly Mammoth 200 Emblem of Herois, no discount for exalted

PVP Mounts - 9 Mounts

* 68 - Black Battlestrider 30 BG marks of WG/AB/AV
69 - Black War Ram 30 BG marks of WG/AB/AV
70 - Black War Steed Bridle 30 BG marks of WG/AB/AV
71 - Reins of the Black War Elekk 30 BG marks of WG/AB/AV
72 - Reins of the Black War Tiger 30 BG marks of WG/AB/AV
73 - Stormpike Battle Charger 50 AV marks
74 - Reins of the Dark Riding Talbuk 70 Halaa Battle Tokens, 15 Halaa Research Token
75 - Reins of the Dark War Talbuk 100 Halaa Battle Tokens, 20 Halaa Research Token
76 - Reins of the Black War Mammoth 300 Stone Keepers Shards

Crafteble mounts - 5 Mounts

* 77 - Mekgineer's Chopper Engineering
78 - Flying Machine Control Engineering only
79 - Turbo-Charged Flying Machine Control Engineering only
80 - Flying Carpet Tailoring only
81 - Magnificent Flying Carpet Tailoring only

Archievement mounts - 6 Mounts

* 82 - Reins of the Black War Bear Complete For the Alliance
83 - Reins of the Albino Drake Complete Leading the Cavalry
84 - Reins of the Violet Proto-Drake Complete What A Long, Strange Trip It's Been
85 - Reins of the Red Proto-Drake Complete Glory of the Hero
86 - Reins of the Plagued Proto-Drake Complete Glory of the Raider
87 - Reins of the Black Proto-Drake Complete Heroic: Glory of the Raider

Drops - 19 Mounts

* 88 - Swift Zulian Tiger Rare drop from High Priest Thekal - Zul'Gerub
89 - Swift Razzashi Raptor Rare drop from Bloodlord Mandokir - Zul'Gerub
90 - Deathcharger's Reins Rare drop from Baron Rivendare - Stratholme
91 - Blue Qiraji Resonating Crystal Common drop from Trash - Temple of Ahn'Qiraj
92 - Green Qiraji Resonating Crystal Common drop from Trash - Temple of Ahn'Qiraj
93 - Red Qiraji Resonating Crystal Rare drop from Trash - Temple of Ahn'Qiraj
94 - Yellow Qiraji Resonating Crystal Common drop from Trash - Temple of Ahn'Qiraj
95 - Swift White Hawkstrider Rare drop from Kael'thas Sunstrider - Magisters' Terrace Heroic
96 - Reins of the Raven Lord Rare drop from Anzu - Sethekk Halls Heroic
97 - Fiery Warhorse's Reins Rare drop from Attumen the Huntsman - Karazhan
98 - Reins of the White Polar Bear Rare drop from Hyldnir Spoils - reward from Gretta the Arbiter's daily quests in Stormpeaks
99 - Grand Black War Mammoth Rare drop from Archavon - Vault of Archavon (opens when you win wintergasp)
100 - Ashes of Al'ar Rare drop from Kael'thas Sunstrider - The Eye
101 - Reins of the Green Proto-Drake Rare drop from Mysterious Egg - Revered with The Oracles to buy it (rare drop from the egg)
102 - Reins of the Blue Proto-Drake Rare drop from Skadi the Ruthless - Utgarde Pinacle
103 - Reins of the Time-Lost Proto-Drake 100% drop Time-Lost Proto-Drake(rare) - Stormpeaks
104 - Reins of the Bronze Drake 100% drop Infinite Corruptor - The Culling of Stratholme Heroic (kill all but the last boss within 25 min for spawn)
105 - Reins of the Black Drake 100% drop from Sarthaion - The Obsidian Sanctum (kill Sarthaion with all 3 mini drakes still alive)
106 - Reins of the Twilight Drake 100% drop Sarthaion - The Obsidian Sanctum Heroic (kill Sarthaion with all 3 mini drakes still alive)
107 - Reins of the Blue Drake Rare drop from Alexstrasza's Gift - The Eye of Eternity
108 - Reins of the Azure Drake Rare drop from Alexstrasza's Gift - The Eye of Eternity Heroic

Seasonal drops - 3 Mounts

* 109 - The Horseman's Reins The Headless Horseman - Scarlet Monastery Graveyard
110 - Great Brewfest Kodo Coren Direbrew - The Black Rock Depths
111 - Swift Brewfest Ram Coren Direbrew - The Black Rock Depths

Recruit a friend - 1 Mount

* 112 - Swift Zhevra use the recruit a friend option in account management and recruit a friend for 2 months

class mounts

deathknight

* Acherus Deathcharger

* From one of the quests in your startingarea
Wing Steed of the Ebon Blade 1000G

paladin

* Warhorse

* trainer
Charger trainer

warlock

* Felsteed

* trainer
Dreadsteed trainer

so its possible

Mountain o’ Mounts cataclysm achievement guide. (Alliance Only)

Darnassus Exalted – 7 Mounts
1. Swift Frostsaber 10g
2. Swift Mistsaber 10g
3. Swift Stormsaber 10g
4. Spotted Frostsaber 1g
5. Striped Dawnsaber 1g
6. Striped Frostsaber 1g
7. Striped Nightsaber 1g

Ironforge Exalted – 6 Mounts
8. Swift Brown Ram 10g
9. Swift Gray Ram 10g
10. Swift White Ram 10g
11. Brown Ram 1g
12. Gray Ram 1g
13. White Ram 1g

Stormwind Exalted – 7 Mounts
14. Swift Brown Steed 10g
15. Swift Palomino 10g
16. Swift White Steed 10g
17. Black Stallion Bridle 1g
18. Brown Horse Bridle 1g
19. Chestnut Mare Bridle 1g
20. Pinto Bridle 1g

Exodar Exalted – 6 Mounts
21. Great Blue Elekk 10g
22. Great Green Elekk 10g
23. Great Purple Elekk 10g
24. Brown Elekk 1g
25. Gray Elekk 1g
26. Purple Elekk 1g

Gnomeregan Exiles Exalted – 7 Mounts
27. Swift Green Mechanostrider 10g
28. Swift White Mechanostrider 10g
29. Swift Yellow Mechanostrider 10g
30. Blue Mechanostrider 1g
31. Green Mechanostrider 1g
32. Red Mechanostrider 1g
33. Unpainted Mechanostrider 1g

Gryphon Mounts – 7 Mounts
34. Swift Blue Gryphon 100g
35. Swift Green Gryphon 100g
36. Swift Purple Gryphon 100g
37. Swift Red Gryphon 100g
38. Ebon Gryphon 50g
39. Golden Gryphon 50g
40. Snowy Gryphon 50g

PvP Mounts – 7 Mounts
41. Black Battlestrider 2000 Honor Points
42. Black War Ram 2000 Honor Points
43. Black War Steed Bridle 2000 Honor Points
44. Black War Elekk 2000 Honor Points
45. Black War Tiger 2000 Honor Points
46. Stormpike Battle Charger 2000 Honor Points
47. Black War Mammoth 2000 Honor Points

Mei Francis – 3 Mounts
48. Armored Snowy Gryphon 2000g
49. Armored Brown Bear 2000g
50. Wooly Mammoth 2175 JP

Leading the Cavalry – 1 Mount
51. Albino Drake Achievement Reward

Ramkahen Exalted – 2 Mounts
52. Tan Riding Camel 100g
53. Brown Riding Camel 100g

Tol Barad dailies – 2 Mounts
54. Spectral Steed 165 Tol Barad Commendations
55. Drake of the West Wind 200 Tol Barad Commendations

Vashj’ir – 1 Mount
56. Abyssal Seahorse Quest reward

Kurenai Exalted – 8 Mounts
57. Cobalt War Talbuk 100g
58. Silver War Talbuk 100g
59. Tan War Talbuk 100g
60. White War Talbuk 100g
61. Cobalt Riding Talbuk 70g
62. Silver Riding Talbuk 70g
63. Tan Riding Talbuk 70g
64. White Riding Talbuk 70g

Sha’tari Skyguard exalted – 5 Mounts
65. Blue Riding Nether Ray 200g
66. Green Riding Nether Ray 200g
67. Purple Riding Nether Ray 200g
68. Red Riding Nether Ray 200g
69. Silver Riding Nether Ray 200g

Netherwing Exalted – 6 Mounts
70. Azure Netherwing Drake Quest reward
71. Cobalt Netherwing Drake 200g
72. Onyx Netherwing Drake 200g
73. Purple Netherwing Drake 200g
74. Veridian Netherwing Drake 200g
75. Violet Netherwing Drake 200g

Wyrmrest Accord Exalted – 1 Mount
76. Red Drake 2000g

Sons of Hodir Exalted – 2 Mounts
77. Reins of the Ice Mammoth 1000g
78. Reins of the Grand Ice Mammoth 10000g

Cenarion Expedition Exalted – 1 Mount
79. Cenarion War Hippogryph 2000g

Wintersaber Trainers Exalted – 1 Mount
80. Reins of the Winterspring Frostsaber Quest

Argent Tournament Mounts – 14 Mounts
81. Argent Warhorse 100 Champion’s Seals
82. Quel’dorei Steed 100 Champion’s Seals
83. Silver Covenant Hippogryph 150 Champion’s Seals
84. Argent Hippogryph 150 Champion’s Seals
85. Darnassian Nightsaber 100 Champion’s Seals
86. Siwft Moonsaber 5 Champion’s Seals + 400g
87. Stormwind Steed 100 Champion’s Seals
88. Swift Gray Steed 5 Champion’s Seals + 400g
89. Exodar Elekk 100 Champion’s Seals
90. Great Red Elekk 5 Champion’s Seals + 400g
91. Ironforge Ram 100 Champion’s Seals
92. Swift Violet Ram 5 Champion’s Seals + 400g
93. Gnomeregan Mechanostrider 100 Champion’s Seals
94. Turbostrider 5 Champion’s Seals + 400g

Expensive Mounts – 3 Mounts
95. Traveler’s Tundra Mammoth 20000g
96. Mekgineer’s Chopper Engineering
97. Sandstone Drake Alchemy

Ahn’ Qiraj Mounts
98. Blue Qiraji Resonation Crystal Common Drop in Ahn’Qiraj
99. Yellow Qiraji Resonating Crystal Common Drop in Ahn’Qiraj
100. Green Qiraji Resonating Crystal Common Drop in Ahn’Qiraj
101. Red Qiraji Resonating Crystal Rare Drop in Ahn’Qiraj

Achievement Mounts – 9 Mounts
102. Drake of the East Wind Glory of the Cataclysm Raider
103. Volcanic Stone Drake Glory of the Cataclysm Hero
104. Black War Bear For The Alliance!
105. Bloodbathed Frostbrood Vanquisher Glory of the Icecrown Raider 10
106. Icebound Frostbrooed Vanquisher Glory of the Icecrown Raider 25
107. Rusted Proto-Drake Glory of the Ulduar Raider 10m
108. Ironbound Proto-Drake Glory of the Ulduar Raider 25m
109. Red Proto Drake Glory of the Hero
110. Violet Proto-Drake Achievement Reward

Drops – 26 Mounts
111. Swift Zulian Panther Zul’Gurub Heroic drop
112. Armored Razzashi Raptor Zul’Gurub Heroic drop
113. Grey Riding Camel Rare Monster
114. Drake of the North Wind Vortex Pinnacle Heroic drop
115. Drake of the South Wind Throne of the Four Winds drop
116. Phosphorescent Stone Drake Rare Monster
117. Subdued Seahorse Rare Monster
118. Amani Battle Bear Zul’Aman Heroic drop
119. Invincible Icecrown Citadel 25m Heroic
120. Grand Black War Mammoth Vault of Archavon drop
121. Fiery Warhorse Karazhan drop
122. Rivendare’s Deathcharger Stratholme drop
123. White Polar Bear Hyldnir Spoils
124. Raven Lord Setthek Halls Heroic Rare drop
125. Swift White Hawkstrider Magister’s Terrace Heroic drop
126. Azure Drake Eye of Eternity drop
127. Black Drake Obsidium Sanctum 10m 3D
128. Blue Drake The Oculus Heroic drop
129. Blue Proto-Drake Utgarde Pinnacle Heroic drop
130. Bronze Drake CoT: CoS Heroic drop
131. Onyxian Drake Onyxia’s Lair drop
132. Time-Lost Proto-Drake Rare mob
133. Twilight Drake Obsidium Sanctum 25m 3D
134. Vitreous Stone Drake Stonecore drop
135. Ashes of Al’ar Tempest Keep drop
136. Mimiron’s Head Ulduar drop
137.Green Proto-Drake Cracked Egg - Oracles Revered

Very-Hard-To-Obtaion Mounts – 3 Mounts
138. Dark Riding Talbuk 70 Halaa Battle Tokens 15 Halaa Research Tokens
139. Dark War Talbuk 100 Halaa Battle Tokens 20 Halaa Research Tokens
140. Crimson Deathcharger Icecrown Citadel Quest reward

Guild Mounts – 2 Mounts
141. Golden King Guild Level 25
142. Dark Phoenix Guild Glory of the Cataclysm Raider

Profession Specific Mounts – 8 Mounts
143. Flying Machine Engineering Only
144. Turbo-Charged Flying Machine Engineering Only
145. Flying Carpet Tailoring Only
146. Magnificent Flying Carpet Tailoring Only
147. Frosty Flying Carpet Tailoring Only
148. Sea Turtle Fishing Only
149. Fossilized Raptor Archaeology Only

Class Specific Mounts – 7 Mounts
150. Archerus Deathcharger Death Knight Only
151. Winged Steed of the Ebon Blade Death Knight Only
152. Argent Charger Paladin Only
153. Warhorse/ Exarch's Elekk Paladin Only
154. Charger/Great Exarch's Elekk Paladin Only
155. Felsteed Warlock Only
156. Dreadsteed Warlock Only

Hope this helps

Here's a breakdown of all the game's currently available mounts (Summary at bottom).

Horde:
29 Racial Mounts (+3 new racials in 3.1)
9 PvP rewards (including Halaa and WG mounts)
7 Windriders
1 Mechano-hog
4 Mounts from Mei Francis
1 Cenarion Hippogryph
8 Mag'har Talbuks
6 Netherdrakes
5 Nether Rays
1 Red Drake (Wyrmrest)
2 Mammoths (Sons of Hodir)
(+1 for the Albino Drake)
=77 mounts readily available for Horde

Alliance:
32 Racial Mounts
9 PvP rewards (including Halaa and WG)
7 Gryphons
1 Mekgineer's Chopper
4 Mounts from Mei Francis
1 Cenarion Hippogryph
8 Kurenai Talbuks
6 Netherdrakes
5 Nether Rays
1 Red Drake (Wyrmrest)
2 Mammoths (Sons of Hodir)
1 Frostsabre (Winterspring)
(+1 for the Albino Drake)
=78 Mounts Readily Available for Alliance

Seasonal:
1 Headless Horseman's Horse
1 Great Brewfest Kodo
1 Swift Brewfest Ram
=Up to 80 (Horde) or 81 (Alliance)

Achievements:
1 Black War Bear (For the Horde)
1 Red Proto-drake (Glory of the Hero)
1 Violet Proto-drake (What a Long, Strange Trip It's Been)
1 Rusted Proto-drake (Glory of the Raider) (Changed to reflect 3.1)
1 Iron-bound Proto-drake (Heroic: Glory of the Raider) (Changed to reflect 3.1)
=Up to 85 (Horde) or 86 (Alliance)

Guaranteed Drops:
1 Black Drake (Regular Sartharion +3 Drakes)
1 Twilight Drake (Heroic Sartharion +3 Drakes)
1 Bronze Drake (Heroic CoT: CoS Timed)
=Up to 88 (Horde) or 89 (Alliance)

AQ:
4 Qiraji Mounts (Relatively high drop chance)
=Up to 92 (Horde) or 93 (Alliance)

Argent Tournament:
5 mounts.
=Up to 97 (Horde) or 98 (Alliance)

Class/Profession:
2 Class Mounts for Death Knights, Warlocks, Paladins
2 Flying Carpets for Tailors
2 Flying Machines for Engineers
=Up to 103 (Horde) or 104 (Alliance)

TCG:
1 Bear
1 Turtle
2 Spectral Tigers
2 Nether Rockets
=Up to 109 (Horde) or 110 (Alliance)

Rare Drops:
14 drops from various bosses/quests/etc.
1 Turtle Mount, rare from Fishing Schools
=Up to 124 (Horde) or 125 (Alliance)

Conclusion:
The only way to get 100 mounts (as of 3.0.8) without farming for rare drops is to be a lock, pally, or DK, have Tailoring AND Engineering, and get all TCG mounts for Horde or 2 TCG mounts for Alliance. Or if you have certain unattainable mounts like the Amani War Bear from ZA, Big Blizzard Bear from Blizzcon '08, the various extremely old racial mounts, or the Arena reward Netherdrakes you can make the process a little easier.

As a Horde, you'll pretty much have to farm rare mounts. You have to get all the class and prof. mounts first of all, and secondly, you won't get the all the TCG mounts without huge luck or enormous real life expense (Spectral Tiger codes go for $750+ while others go for $100+). And if you get none of those mounts, be prepared for a tough run because you'll have to farm 12/14 of the avaialable mounts in order to procure this achievement.

As an Alliance, you'll have a slightly easier time, but without class or prof. mounts you'll still have to farm 8/14 rare mounts.

As a side note, only 4 of the rare drops are easily soloable, Green Proto-drake, Time-lost Proto-drake, Rivendare's Deathcharger, and White Polar Bear. The rest require at minimum a small group of 3-5 (ZG mounts, White Hawkstrider, Attuman's Steed, etc.), or raid groups (Malygos drops, Grand Black War Mammoth, Ashes of Al'ar, etc.). Certain classes at 80 might be able to solo ZG or maybe Magister's Terrace, but most can't.

Hope this helps.

(Quoted from my post on the alliance page)

NEW AS OF 3.1: It seems as though the gab between Alliance and Horde has been closed a fair bit, however, without class/prof/TCG mounts, you're still likely to need to farm a few rare drops.

Edited for corrections and 3.1 updates.
Edit 2: Forgot Argent Tournament mounts.

If you see any mistakes our mounts I missed please let me know. Exceptions are the Arena Season rewards and unobtainable racial mounts (Ivory Raptor, etc.)