55 Exalted Reputations

Actually, it's possible for anyone to get this achievement using only those reputations that are still available in-game. There are a total of 43 neutral factions (of which you can have 41 at exalted at any given time, due to directly-opposed factions), 19 Horde-only factions, and 19 Alliance-only factions.

Neutral Factions

01) Argent Crusade
02) Argent Dawn
03) Ashtongue Deathsworn
04) Avengers of Hyjal
05) Bloodsaul Buccaneers
06) Booty Bay
07) Brood of Nozdormu
08) Cenarion Circle
09) Cenarion Expedition
10) Darkmoon Faire
11) Everlook
12) Frenzyheart Tribe OR The Oracles
13) Gadgetzan
14) Guardians of Hyjal
15) Guild
16) Hydraxian Waterlords
17) Keepers of Time
18) Kirin Tor
19) Knights of the Ebon Blade
20) Lower City
21) Netherwing
22) Ogri'la
23) Ramkahen
24) Ratchet
25) Ravenholdt
26) Sha'tari Skyguard
27) Shattered Sun Offensive
28) Sporeggar
29) The Aldor OR The Scyers
30) The Ashen Verdict
31) The Consortium
32) The Earthen Ring
33) The Kalu'ak
34) The Scale of the Sands
35) The Sha'tar
36) The Sons of Hodir
37) The Violet Eye
38) The Wyrmrest Accord
39) Therazane
40) Thorium Brotherhood
41) Timbermaw Hold

Horde-Only Factions

42) Bilgewater Cartel
43) Darkspear Trolls
44) Dragonmaw Clan
45) Frostwolf Clan
46) Hellscream's Reach
47) Horde Expedition
48) Orgrimmar
49) Silvermoon City
50) The Defilers
51) The Hand of Vengeance
52) The Mag'har
53) The Sunreavers
54) The Taunka
55) Thrallmar
56) Thunder Bluff
57) Tranquillien
58) Undercity
59) Warsong Offensive
60) Warsong Outriders

Alliance-Only Factions

42) Alliance Vanguard
43) Baradin's Wardens
44) Darnassus
45) Exodar
46) Explorer's League
47) Gilneas
48) Gnomeregan
49) Honor Hold
50) Ironforge
51) Kurenai
52) Silverwing Sentinels
53) Stormpike Guard
54) Stormwind
55) The Frostborn
56) The League of Arathor
57) The Silver Covenant
58) The Valiance Expedition
59) Wildhammer Clan
60) Wintersaber Trainers

Used to award "the Beloved" title, but changed to "70 Exalted reps" during beta.

As of Cataclysm it's possible for some player to get 61 Exalted factions, however Zandalar Tribe and Shen'dralar are no longer obtainable, so it leaves us with 59.

For good overview, here is Wowhead's guide:
[guide=12 domain=mop]

Just to clear up any possible confusion, the Zandalar and Shen'dralar reputations will still count towards the rep achievements if you reached exalted before the factions were removed.