Rule of thumb: Take your current skill level and divide it by 5 to know what level of mobs you currently can skin.

Visit a Skinning Trainer located in World of Warcraft, and train for Skinning Apprentice.

Don’t forget to buy the skinning knife. It is not necessary to equip this item to skin.

1-25

Horde

Orcs and Trolls = Mottled Boars and Clattering Scorpids around Sen’Jin Village
Tauren = Plainstriders around Bloodhoof Village

Alliance

Humans = Stonetusk Boars around Goldshire
Gnomes and Dwarves = Crag Boars and Wendigo south of Kharanos
Night Elves = Nightsabers around Dolanaar

25-50

Horde

Undead = Mottled Worgs and Moonrage Gluttons around Silverpine
Orcs and Trolls = Elder Mottled Boars, Venomtail Scorpids, and Dreadmaw Crocolisks around Orgrimmar
Tauren = Flatland Prowlers and Prairie Wolf Alpha around Thunderbluff

Alliance

Human = Prowlers and Young Forest Bears around Eastvale Logging Camp
Gnomes and Dwarves = Snow Tracker Wolves around Kharanos.
Night Elves = Moonstalker Runt and Thistle Bears around Auberdine

50-100

Horde

Fleeting Plainstriders and Savannah Prowlers around Crossroads

Alliance

Humans = Goretusks all around Sentinel Hill.
Gnomes and Dwarves = Grizzly Black Bears and Loch Crocolisks around Thelsamar
Night Elves = Moonstalker Sire north of Auberdine

100-130

Horde

Stormsnouts and Thunderhawk Hatchling around Camp Taurajo

Alliance

Wetland Crocolisks and Mottled Raptors around Bluegill Marsh and Whelgar’s Excavation Site

130-150

Alliance and Horde

Elder Gray Bears and Mountain Lions around Hillsbrad Foothills
Elder Ashenvale Bears, Elder Shadowhorn Stags and Ghostpaw Howler in Ashenvale

150-170

Alliance and Horde

Yeti Cave in Hillsbrad Foothills
Pesterhide Hyenas, Lions, Highperch Wyvern and Thunderhawks in Thousand Needles

170-180

Alliance and Horde

Raptors in Arathi Highlands
Turtles and Saltstone Basilisks in The Shimmering Flats

180-220

Alliance and Horde

Lashtail Raptors, Panthers and Elder Stranglethorn Tigers around Nessingwarys Camp in Stranglethorn Vale
(You can get your skinning all the way up to 300 as the mobs in this area range from level 34 to level 50)

220-250

Alliance and Horde

Raptors and Elder Mistvale Gorillas around the Gurabashi Arena
Panthers, Jaguars and Crocs in Swamp of Sorrows.
Dragonkin, Coyotes and Ridge Stalkers/Huntresses in Badlands.

250-275

Alliance and Horde

Snickerfangs and Boars in North Blasted Lands
Silvermanes and Gryphons in The Hinterlands.
Stags and Hippogryphs in Azshara.
Hippogryphs, Apes, Bears, Wolves, Screechers and Yetis in Feralas.

275-300

Alliance and Horde

Yetis, Chimeras and Bears in Winterspring
Bears in Western Plaguelands
Plaguehounds and Plaguebats in Eastern Plaguelands

300-375

Burning Crusade Skinning

Start heading to Thrallmar and search for Moorutu if you are on Horde, he's going to be able to teach you Master Skinning. For Alliance players they will need to go to Honor Hold and find Jelena Nightsky.

It is very easy to go from 300 to 375, it is just a matter of patience and time for the simple reason that even if your skinning orange mobs, you’ll only get a skill up every 5-7 successful skins.

301-310
Hellboars around Hellfire Citadel in Hellfire Peninsula.

310-330
Quillfang Ravagers around Falcon Watch in Hellfire Peninsula.

330-350
Talbuk Thorngrazer and Clefthoof Bull all around Nagrand.

350-375
Nether Drakes around Stormspire in Netherstorm
Bladespire Raptors and Scalewing Serpents around Blades Edge Mountains.

375-450

Wrath of the Lich King Skinning

Just start out in the Borean Tundra or Howling Fjord at around level 350 if you chose to not get to 375 in The Burning Crusade areas.

Skinning Level  375-405
Shoveltusks in Howling Fjord

Skinning Level  375-405
Mammoths in Borean Tundra

405-430
Deer, Infected Grizzly Bears, Wolves, and any other mob all over Grizzly Hills

430-450
Giraffes, Mangal Crocolisks, Gorillas, and any other mob in Sholazar Basin