Skinning is an excellent money maker in WoW and also provides the raw materials for leatherworking, and some bits and pieces for other professions. Prices on some of the higher level skinned items (eg: Cobra Scales) out price nearly any other gathered item.

Also, since you are going to be killing so many beasts in this game you won't have to do much to make some good cash through your skinning profession, even if the prices get a bit low at times. Skin everything you kill and you won't have to pay much attention to what level your skill is, it will always be high enough, even if you're blasting through the levels with something like the iDemise leveling guide.

1 - 25
Horde
Undead = Hounds around Brill
Orcs and Trolls = Mottled Boars and Scorpids around Sen'Jin Village
Tauren = Prowlers and Plainstriders around Bloodhoof Village

Alliance
Humans = Boars around Goldshire
Gnomes and Dwarves = Crag Boars and Wendigo's South of Kharanos
Night Elves = Nightsabers and critters around Dolanaar

26 - 50
Horde
Undead = Worgs and Moonrage Gluttons around Silverpine
Orcs and Trolls = Boars, Scorpids, Crocolisks and Raptors around Orgrimmar
Tauren = Prowlers and Prairie Wolves around Thunderbluff

Alliance
Human = Prowlers and Bears around Eastvale Logging Camp
Gnomes and Dwarves = Wolves around Brenwall Village.
Night Elves = Moonstalkers and Bears around Auberdine

51 - 100
Horde
Plainstriders, Raptors and Prowlers around Crossroads.

Alliance
Humans = Goretusks all around Sentinel Hill.
Gnomes and Dwarves = Bears and Crocolisks around Thelsamar
Night Elves = Moonstalkers and Bears North of Auberdine

101 - 130
Horde
Stormsnouts and Thunderhawks around Camp Taurajo

Alliance
Crocolisks and Raptors around Bluegill Marsh and Whelgar's Excavation Site
Alternatives:
Whelps and boars around Lakeshire for Alliance.

131 - 150
Bears and Mountain Lions around Hillsbrad Foothills
Alternatives:
Ravagers and Wolves in Duskwood if your Alliance.
Bears, Stags and Ghostpaws in Ashenvale.

151 - 170
Yeti Cave in Hillsbrad Fields and Mountain Lions on the "Daggers" (these are the bits of land between Hillsbrad and Alterac Mountains, one is called Corrans Dagger, so hence the nickname)
Alternatives:
Hyenas, Lions, Wyvern and Thunderhawks in Thousand Needles.
Bears, Stags and Ghostpaws in Ashenvale.

171 - 180
Raptors in Arathi Highlands.
Alternatives:
Turtles and Basilisks in The Shimmering Flats.

181 - 220
Raptors, Panthers and Tigers around Nessingwarys Camp in Stranglethorn Vale.
Alternatives:
Raptors and Crocs in Dustwallow Marsh.
Thunder Lizards, Kodos, Basilisks, Scorpids and Hyenas in Desolace.
Whelps in Swamp of Sorrows.

221 - 250
Raptors and Gorillas around the Gurabashi Arena
Alternatives:
Panthers, Jaguars and Crocs in Swamp of Sorrows.
Dragonkin, Coyotes and Ridge Stalkers/Huntresses in Badlands.
Wolves around Feathermoon Stronghold in Feralas if your Alliance.

251 - 275
Snickerfangs and Boars in North Blasted Lands
Alternatives:
Silvermanes and Gryphons in The Hinterlands.
Stags and Hippogryphs in Azshara.
Hippogryphs, Apes, Bears, Wolves, Screechers and Yetis in Feralas.

276 - 300
Jagueros and Gorillas on Jaguero Island.
Alternatives:
Yetis, Chimeras and Bears in Winterspring.
Bears in Western Plaguelands.
Plaguehounds and Plaguebats in Eastern Plaguelands.
Turtles by Raventusk Village in The Hinterlands.
Turtles and Chimeras in Azshara.
Dragonkin, Worgs and Scorpids in Burning Steppes.

This is a mob level to leather type correlation
Ruined Leather Scraps: 1-16
Light Leather: 1-27
Light Hide: 10-27
Medium Leather: 15-36
Medium Hide: 15-36
Heavy Leather: 25-46
Heavy Hide: 25-46
Thick Leather: 35-63
Thick Hide: 40-59
Rugged Leather: 43-63
Rugged Hide: 47-63
300-375
Truthfully I'd say that 300 - 375 skill is probably the easiest level range, or at the least the most profitable as well as fun. They provide tons of cash, can be accomplished whilst leveling 60-70, and due to the high mob count in each zone aren't exactly hard to complete, however at the same time they can possibly take the longest out of all the skill levels, perhaps even longer than 1-300. However even that said you could possibly hit 375 skill purely within Hellfire Peninsula.

301 - 310

Hellboars around Hellfire Citadel in Hellfire Peninsula.

311 - 330

Ravagers around Falcon Watch in Hellfire Peninsula.

331 - 350

Talbuk's and Clefthoofs all over Nagrand. (you could just as easily continue skinning to 375 here if you want, as if wont take that much longer, than going to Netherstorm and skinning Drakes)

351 - 375

Netherdrakes around Stormspire in Netherstorm or around Netherwing Fields in Shadowmoon Valley or Raptors and Wind Serpents around Blades Edge Mountains.

Penn's Professions Guide
With Penn's Professions Guide you have a resource which will show you how to level any skill in WoW as quickly, efficiently, and as cheaply as possible. Let's face it, some of these professions are expensive to level. In addition, you will learn which professions work best with each other and which are the best for raking in the gold.

So if you're interested in exploring professions other than skinning you should treat yourself to a copy of Penn's Guide and make your profession leveling a lot easier.