Locations of each type of normal Vein:

Copper - Alterac Mountains, Ashenvale, Darkshore, Desolace, Dun Morogh, Durotar, Duskwood, Elwynn Forest, Hillsbrad Foothills, Loch Modan, Mulgore, Redridge Mountains, Silverpine Forest, Stonetalon Mountains, The Barrens, Thousand Needles, Tirisfal Glades, Westfall, and Wetlands

Tin - Alterac Mountains, Arathi Highlands, Ashenvale, Darkshore, Desolace, Duskwood, Hillsbrad Foothills, Loch Modan, Redridge Mountains, Silverpine Forest, Stonetalon Mountains, Stranglethorn Vale, The Barrens, Thousand Needles, Westfall, and Wetlands

Iron - Alterac Mountains, Arathi Highlands, Ashenvale, Badlands, Blasted Lands, Desolace, Duskwood, Dustwallow Marsh, Feralas, Hillsbrad Foothills, Searing Gorge, Stonetalon Mountains, Stranglethorn Vale, Swamp of Sorrows, Tanaris, The Hinterlands, Thousand Needles, and Wetlands

Mithril Deposit - Alterac Mountains, Arathi Highlands, Azshara, Badlands, Blasted Lands, Burning Steppes, Desolace, Dustwallow Marsh, Eastern Plaguelands, Felwood, Feralas, Hillsbrad Foothills, Searing Gorge, Silithus, Stonetalon Mountains, Stranglethorn Vale, Swamp of Sorrows, Tanaris, The Hinterlands, Thousand Needles, Western Plaguelands, and Winterspring

Small Thorium Vein - Blasted Lands, Burning Steppes, Eastern Plaguelands, Felwood, Feralas, Searing Gorge, Silithus, Tanaris, The Hinterlands, Un'Goro Crater, Western Plaguelands, and Winterspring

Rich Thorium Vein - Azshara, Burning Steppes, Eastern Plaguelands, Silithus, Un'Goro Crater, Western Plaguelands, and Winterspring

Locations of each type of uncommon Vein:

Silver - Alterac Mountains, Arathi Highlands, Ashenvale, Badlands, Darkshore, Desolace, Duskwood, Dustwallow Marsh, Feralas, Hillsbrad Foothills, Loch Modan, Redridge Mountains, Searing Gorge, Silverpine Forest, Stonetalon Mountains, Stranglethorn Vale, Swamp of Sorrows, Tanaris, The Barrens, The Hinterlands, Thousand Needles, Westfall, and Wetlands

Gold - Alterac Mountains, Arathi Highlands, Ashenvale, Azshara, Badlands, Blasted Lands, Burning Steppes, Desolace, Duskwood, Dustwallow Marsh, Eastern Plaguelands, Felwood, Feralas, Hillsbrad Foothills, Searing Gorge, Silithus, Stonetalon Mountains, Stranglethorn Vale, Swamp of Sorrows, Tanaris, The Hinterlands, Thousand Needles, Western Plaguelands, Wetlands, and Winterspring

Truesilver - Alterac Mountains, Arathi Highlands, Azshara, Badlands, Blasted Lands, Burning Steppes, Desolace, Dustwallow Marsh, Eastern Plaguelands, Felwood, Feralas, Searing Gorge, Silithus, Stonetalon Mountains, Stranglethorn Vale, Swamp of Sorrows, Tanaris, The Hinterlands, Un'Goro Crater, Western Plaguelands, and Winterspring

Location and Purpose of Special Veins:

Rethban Ore - Any Copper or Tin mine in Redridge Mountains will drop these randomly.

Rethban Ore's for a quest given by Foreman Oslow, in Redridge Mountains. He should be located at the southeast side of Lakeshire. This isn't really related to mining, since mobs will drop it just as frequently, but I added it by request.

Incendicite - Wetlands, in the cave directly north of Dun Algaz on the map.

Incendicite is the objective of the alliance quest Search for Incendicite, which is given to you by Pilot Stonegear in Dun Morogh.

Indurium - Inside Uldaman, in the various tunnels.

Indurium is the objective of the neutral quest Indurium Ore given by Pozzik at the race track in Thousand Needles.

Lesser Bloodstone - Arathi Highlands, in the northeast corner of the map.

Lesser Bloodstone Ore is the objective of the alliance quest Favor for Krazek, given by Krazek in Booty Bay.

Dark Iron - In Blackrock Depths and Molten Core, deposits can be found in any of the numerous caverns.

Dark Iron serves 2 purposes. You can either smelt it to create bars for any of the Blackrock Depths exclusive recipes, or you can turn it in to Lokhtos Darkbargainer in the bar in Blackrock Depths to increase your Thorium Brotherhood faction. When you get your Thorium Brotherhood faction to Honored and above, Lokhtos will sell you some really nice crafting recipes. Before you get too excited about that prospect, read the paragraph below about smelting Dark Iron Ore.

To create one Dark Iron Bar, you need 8 Dark Iron Ore, and you can only smelt Dark Iron at the Dark Forge, which is located near the portal to Molten Core. Before you can smelt it, you need to learn how to smelt Dark Iron Ore from Gloom'rel deep in Blackrock Depths in the 7 Ghosts room. He'll teach you how to smelt it if you give him 20 Gold Bars, 10 Truesilver Bars, and 2 Star Rubies. You can only make items that require Dark Iron Bars at the Black Anvil, which is on the other side of the instance where Lord Incendius is located.

Gems found in each type of Vein:

Copper - Malachite, Shadowgem, Tigerseye
Tin - Jade, Shadowgem, Lesser Moonstone, Moss Agate, Blood Shard(can only be mined in the Barrens, used for a quest)
Silver - Shadowgem, Lesser Moonstone, Moss Agate
Iron - Aquamarine, Jade, Lesser Moonstone, Citrine
Gold - Jade, Lesser Moonstone, Citrine
Mithril - Aquamarine, Citrine, Black Vitriol, Star Ruby
Truesilver - Aquamarine, Citrine, Star Ruby
Dark Iron - Black Diamond, Blood of the Mountain, Black Vitriol
Small Thorium - Large Opal, Blue Sapphire, Star Ruby, Black Vitriol
Rich Thorium - Arcane Crystal, Azerothian Diamond, Blue Sapphire, Huge Emerald, Large Opal, Star Ruby

Most gems you find are only used in crafting, and can be bought or sold in the AH cheap.

However, a few gems are extremely rare and therefore valuable:

Arcane Crystals - Anywhere from 20-40g depending on your server. Drop rate is approximately 3%, although their droprate was reportedly changed in the last patch.

Azerothian Diamonds - Anywhere from 40-100g depending on your server. Drop rate is approximately 1%.

Blood of the Mountain - Anywhere from 50-150g dpending on your server. Drop rate is approximately 1%.

Tips

-Use Thottbot if you need any information regarding Mining or just about anything else.

-If you play on a PvP server, stay out of popular zones when trying to raise your skill. Stay away from Hillsbrad Foothills, Stranglethorn Vale, and Arathi Highlands unless you're questing there.

-Try to avoid Silithus when you're looking for Rich Thorium Veins. Most of them are underground, and you have to fight through numerous elite mobs to reach them.

-If you're looking for Rich Thorium Veins, try looking in Un'Goro Crater, Burning Steppes, Eastern Plaguelands, and Azshara first. Those zones seem to have the most Thorium veins, and they're easy to navigate.

-If you can't gain anymore skill in a zone, don't go to a zone above your level looking for the next tier of ore. If you go to a zone that's too high level for you, you'll waste a lot of time running back to your corpse. Get a few levels, then move on to the next zone.

-Download the Gatherer and the Repository from:
http://norgs.internutter.org/gatherer.htm and
http://gather.reet.org/

This addon is extremely helpful, and it'll save you a lot of time.

-Don't give up if it takes you a long time to find Arcane Crystals or Azerothian Diamonds. It's completely random whether they drop or not, so it may take awhile before you get your first one. Also, don't forget that they only drop from Rich Thorium Veins, so don't expect to see one drop off a small one.