While this guide was originally written for the Leading the Cavalry achievement to help players get their hands on [Reigns of the Albino Drake], there's a new, hip kid in town -- Mountain o' Mounts -- and it rewards yet another special mount.  This time, Alliance and Horde each receive their own mount -- the [Blue Dragonhawk Mount] for Alliance and the [Red Dragonhawk Mount] for Horde.  The tabs below are separated based on faction: Alliance and Horde.  Click on the tab you'd like to browse for all of the mounts available to that respective faction.  You'll notice some overlap, but this is obviously intended because of many mounts being available to both factions.

Note that for new characters this will be an extremely difficult achievement to obtain due to the number of mounts no longer available.  You could also potentially see a monetary cost due to a handful of the mounts only being available through the World of Warcraft Trading Card Game.

Total Possible Mounts: 128 (Not counting class mounts)

General Mounts (50)

Classic (7)

 Mount  Source
 Deathcharger’s Reins  Stratholme – drops from Baron Rivendare
 Swift Zulian Tiger  Zul’Gurub – drops from High Priest Thekal
 Swift Razzashi Raptor  Zul’Gurub – drops from Bloodlord Mandokir
 Blue Qiraj Resonating Crystal  Temple of Anh-Qiraj (AQ40) – random trash drop
 Green Qiraj Resonating Crystal  Temple of Anh-Qiraj (AQ40) – random trash drop
 Red Qiraj Resonating Crystal  Temple of Anh-Qiraj (AQ40) – random trash drop
 Yellow Qiraj Resonating Crystal  Temple of Anh-Qiraj (AQ40) – random trash drop

The Burning Crusade (26)

 Mount  Source
 Colbalt Riding Talbuk  Nagrand – 70g + Exalted Kurenai
 Silver Riding Talbuk  Nagrand – 70g + Exalted Kurenai
 Tan Riding Talbuk  Nagrand – 70g + Exalted Kurenai
 White Riding Talbuk  Nagrand – 70g + Exalted Kurenai
 Colbalt War Talbuk  Nagrand – 100g + Exalted Kurenai
 Silver War Talbuk  Nagrand – 100g + Exalted Kurenai
 Tan War Talbuk  Nagrand – 100g + Exalted Kurenai
 White War Talbuk  Nagrand – 100g + Exalted Kurenai
 Dark Riding Talbuk  Halaa – 70 Halaa Battle Token 15 Halaa Reseach Token
 Dark War Talbuk  Halaa – 100 Halaa Battle Token 20 Halaa Reseach Token
 Blue Riding Nether Ray  Terokkar Forest – 200g + Exalted Sha’tari Skyguard
 Green Riding Nether Ray  Terokkar Forest – 200g + Exalted Sha’tari Skyguard
 Purple Riding Nether Ray  Terokkar Forest – 200g + Exalted Sha’tari Skyguard
 Red Riding Nether Ray  Terokkar Forest – 200g + Exalted Sha’tari Skyguard
 Silver Riding Nether Ray  Terokkar Forest – 200g + Exalted Sha’tari Skyguard
 Azure Netherwing Drake  Shadowmoon Valley – 200g + Exalted Netherwing
 Cobalt Netherwing Drake  Shadowmoon Valley – 200g + Exalted Netherwing
 Onyx Netherwing Drake  Shadowmoon Valley – 200g + Exalted Netherwing
 Purple Netherwing Drake  Shadowmoon Valley – 200g + Exalted Netherwing
 Veridian Netherwing Drake  Shadowmoon Valley – 200g + Exalted Netherwing
 Violet Netherwing Drake  Shadowmoon Valley – 200g + Exalted Netherwing
 Cenarion War Hippogryph  Zangarmarsh – 1800g + Exalted Cenarion Expedition
 Fiery Warhorse’s Reins  Karazhan – Attumen the Huntsman
 Reins of the Raven Lord  Heroic: Sethekk Halls – Anzu (Druid summoned)
 Swift White Hawkstrider  Heroic: Magister’s Terrace – Kael’thas Sunstrider
 Ashes of Al’ar
 Tempest Keep (Raid: 25) – Kael’thas Sunstrider

Wrath of the Lich King (17)

 Mount  Source
 Armored Brown Bear  Dalaran – 750g
 Black War Bear  Achievement: For the Horde! / For the Alliance!
 White Polar Bear
 Storm Peaks - Rare from Hyldnir Spoils
 Wooly Mammoth  Dalaran – 200 Emblems of Heroism
 Traveler’s Tundra Mammoth  Dalaran – 20,000g (16,000g at Exalted Kirin Tor)
 Black War Mammoth  Wintergrasp – 300 Stone Keeper’s Shards
 Grand Black War Mammoth  Wintergrasp – Archavon the Stone Watcher
 Ice Mammoth  Storm Peaks – 250g + Revered Sons of Hodir
 Grand Ice Mammoth  Storm Peaks – 8,000g + Exalted Sons of Hodir
 Red Drake  Dragonblight – 2,000g + Exalted Wyrmrest Accord
 Blue Proto-Drake  Utgarde Pinnacle – Skadi the Ruthless
 Green Proto-Drake  Rare hatch from Mysterious Egg (Revered+ The Oracles)
 Time-Lost Proto-Drake  Storm Peaks – Time-Lost Proto-Drake
 Black Proto-Drake  Achievement: Heroic: Glory of the Raider
 Red Proto-Drake  Achievement: Glory of the Hero
 Plagued Proto-Drake  Achievement: Glory of the Raider
 Violet Proto-Drake  Achievement: What a Long, Strange Trip It's Been

Seasonal (3)

 Mount  Source
 Swift Brewfest Ram  Corin Direbrew during Brewfest
 Great Brewfest Kodo  Corin Direbrew during Brewfest
 The Horseman’s Reins  The Headless Horseman during Hallow’s End

World of Warcraft Trading Card Game Mounts (6)

 Mount  Source
 Big Battle Bear  The Red Bearon from “Drums of War”
 Riding Turtle  Saltwater Snapjaw from “Heroes of Azeroth”
 Spectral Tiger  Spectral Tiger from “Fires of Outland”
 Swift Spectral Tiger  Spectral Tiger from “Fires of Outland”
 X-51 Nether-Rocket  X-51 Nether-Rocket from “Servants of the Betrayer”
 X-51 Nether-Rocket X-TREME  X-51 Nether-Rocket from “Servants of the Betrayer”

Promotional Mounts (1)

 Mount  Source
 Swift Zhevra  Blizzard’s Recruit-a-Friend Promotion

Class-specific Mounts (6)

 Mount  Source
 Felsteed  Warlock
 Dreadsteed  Warlock
 Warhorse  Paladin
 Charger  Paladin
 Acherus Deathcharger  Death Knight
 Winged Steed of the Ebon Blade  Death Knight

Profession-specific Mounts (4)

 Mount  Source
 Flying Carpet  BoP mount crafted by Tailors at 410 skill
 Magnificent Flying Carpet  BoP mount crafted by Tailors at 415 skill
 Flying Machine  BoP mount crafted by Engineers at 365 skill
 Turbo-Charged Flying Machine  BoP mount crafted by Engineers at 375 skill

Alliance-only Mounts (47)

Reputation-based mounts are initially only available to players of that race.  Human for Stormwind, Dwarf for Ironforge, etc.  However, you can complete many quests to raise your reputation to the required level of Exalted to purchase mounts outside of your home reputation, including repeatable [Runecloth] turn-ins via the Additional Runecloth quests found in each major city.

Stormwind City Reputation (7)

 Mount  Source
 Brown Horse  Katie Hunter in Elwynn Forest – 10g
 Chesnut Mare  Katie Hunter in Elwynn Forest – 10g
 Pinto  Katie Hunter in Elwynn Forest – 10g
 Black Stallion  Unger Statforth in Wetlands – 10g
 Swift Brown Steed  Katie Hunter in Elwynn Forest – 100g
 Swift Palamino  Katie Hunter in Elwynn Forest – 100g
 Swift White Steed  Katie Hunter in Elwynn Forest – 100g

Ironforge Reputation (6)

 Mount  Source
 Brown Ram  Veron Amberstill in Dun Morogh – 10g
 Gray Ram  Veron Amberstill in Dun Morogh – 10g
 White Ram  Veron Amberstill in Dun Morogh – 10g
 Swift Brown Ram  Veron Amberstill in Dun Morogh – 100g
 Swift Gray Ram  Veron Amberstill in Dun Morogh – 100g
 Swift White Ram  Veron Amberstill in Dun Morogh – 100g

Darnassus Reputation (6)

 Mount  Source
 Spotted Frostsaber  Lelanai in Darnassus – 10g
 Striped Frostsaber  Lelanai in Darnassus – 10g
 Striped Nightsaber  Lelanai in Darnassus – 10g
 Swift Frostsaber  Lelanai in Darnassus – 100g
 Swift Mistsaber  Lelanai in Darnassus – 100g
 Swift Stormsaber  Lelanai in Darnassus – 100g

Exodar Reputation (6)

 Mount  Source
 Brown Elekk  Torallius the Pack Handler in Azuremyst Isle – 10g
 Gray Elekk  Torallius the Pack Handler in Azuremyst Isle – 10g
 Purple Elekk  Torallius the Pack Handler in Azuremyst Isle – 10g
 Great Blue Elekk  Torallius the Pack Handler in Azuremyst Isle – 100g
 Great Green Elekk  Torallius the Pack Handler in Azuremyst Isle – 100g
 Great Purple Elekk  Torallius the Pack Handler in Azuremyst Isle – 100g

Gnomeregan Reputation (7)

 Mount  Source
 Blue Mechanostrider  Milli Featherwhistle in Dun Morogh – 10g
 Green Mechanostrider  Milli Featherwhistle in Dun Morogh – 10g
 Red Mechanostrider  Milli Featherwhistle in Dun Morogh – 10g
 Unpainted Mechanostrider  Milli Featherwhistle in Dun Morogh – 10g
 Swift Green Mechanostrider  Milli Featherwhistle in Dun Morogh – 100g
 Swift White Mechanostrider  Milli Featherwhistle in Dun Morogh – 100g
 Swift Yellow Mechanostrider  Milli Featherwhistle in Dun Morogh – 100g

Player versus Player (6)

 Mount  Source
 Stormpike Battle Charger  Alterac Valley - 50 AV Marks
 Black Battlestrider  Stormwind – 30 Marks from AV, AB, & WSG
 Black War Elekk  Stormwind – 30 Marks from AV, AB, & WSG
 Black War Ram  Stormwind – 30 Marks from AV, AB, & WSG
 Black War Steed  Stormwind – 30 Marks from AV, AB, & WSG
 Black War Tiger  Stormwind – 30 Marks from AV, AB, & WSG

Other (10)

 Mount  Source
 Winterspring Frost Saber  Rivern Frostwind in Winterspring – 100g
 Ebon Gryphon  Brunn Flamebeard in Shadowmoon Valley – 100g
 Golden Gryphon  Brunn Flamebeard in Shadowmoon Valley – 100g
 Snowy Gryphon  Brunn Flamebeard in Shadowmoon Valley – 100g
 Swift Blue Gryphon  Brunn Flamebeard in Shadowmoon Valley – 200g
 Swift Green Gryphon  Brunn Flamebeard in Shadowmoon Valley – 200g
 Swift Purple Gryphon  Brunn Flamebeard in Shadowmoon Valley – 200g
 Swift Red Gryphon  Brunn Flamebeard in Shadowmoon Valley – 200g
 Armored Snowy Gryphon  Mei Francis in Dalaran – 2,000g (less with Kirin Tor rep)
 Mekgineer’s Chopper  BoE mount crafted by Engineers at 470 skill

No Longer Available/World Event Mounts (16)

While many of these mounts are no longer obtainable, they do count toward the achievement if you were able to get one while they were available.  However, both the [Big Blizzard Bear] and the [Black Qiraji Resonating Crystal] are, in some cases, still obtainable.

 Mount  Source
 Palomino  Old Epic Mount
 White Stallion  Old Epic Mount
 Black Ram  Old Epic Mount
 Frost Ram  Old Epic Mount
 Ancient Frostsaber  Old Epic Mount
 Nightsaber  Old Epic Mount
 Icy Blue Mechanostrider Mod A  Old Epic Mount
 White Mechanostrider Mod B  Old Epic Mount
 Amani War Bear  Zul’Aman – timed reward (not available post-3.0)
 Brewfest Ram  2007 Brewfest token reward
 Swift Nether Drake  Arena Season 1 Reward
 Merciless Nether Drake  Arena Season 2 Reward
 Vengeful Nether Drake  Arena Season 3 Reward
 Brutal Nether Drake  Arena Season 4 Reward
 Black Qiraji Resonating Crystal  Reward for Bang a Gong! AQ gates opening quest*
 Big Blizzard Bear  2008 BlizzCon Promo**

* If you found a newer server where the gates of Ahn Qiraji hadn’t yet been opened, you could still technically get this mount.
** The 2008 BlizzCon Promo was a card given out to anyone who attended BlizzCon or watched via DIRECTV.  However, there are also various other ways of finding the card, such as website contests.