Copper Ore farming

Copper Ore is the lowest level ore that you can farm. It comes from Copper Veins and mostly found at the starting areas and in lower level zones.
There is not much difference between the zones where you can farm Copper Ore, but the zones listed below are slightly better than the other alternatives. If you are below level 20, you should stay at the zone where you are questing currently, there will be plenty of Copper Ore there.

Copper Ore

Durotar - Horde

Durotar is an excellent place to farm Copper Ore, there are a few caves in this zone and usually there are 3-4 Copper Veins inside those caves.

Darkshore - Alliance

Darkshore is the best place for Alliance players. Even Horde players can go there with flying mount. I was able to get 200 Copper Ore with just one lap in this zone.

Tin Ore farming

Tin Ore is the second-easiest ore to mine, you will need 50 Mining to mine Tin. You can use your smelting ability and turn all your Tin Ore into Tin Bar. This farming guide will list the places where I was able to farm the most amount of Tin in the least amount of time. Farming Tin Ore will be easy because there is loads of it in most lower level zone.

Tin Ore

Hillsbrad Foothills

Alterac Mountains in Hillsbrad Foothills is simply the best place to mine Tin Ore. The place is marked with red on the map. If you run out of Veins, just do a lap around the mountains until they respawn. This place can be a bit harder to reach for lower level Alliance players because it's a horde zone.

Northern Stranglethorn

Northern Stranglethorn is a great alternative if you can't go to Hillsbrad for some reason, but I prefer Hillsbrad.
These are the best zones if you want to farm Tin Ore

Iron Ore farming

Mining Iron Ore requires minimum mining skill of 100. Iron Deposits may be found in many areas where the typical creature level is between about 25 and 35. This Iron Ore farming guide will list the places where you can get the most Iron.

Iron Ore

Feralas

You will find Iron anywhere you go in Feralas, it's the best place to mine Iron. You could actually just do laps at the northern area without going to the southern area.

Western Plaguelands

Western Plaguelands is also an excellent place to farm Iron, just don't go to Hearthglen because there is no ore there. Stick to route I recommend.
These are the best zones if you want to farm Iron Ore.

Mithril Ore farming

This Mithril Ore farming guide will list the places where I was able to farm the most Mithril in the least amount of time. Mithril Ore requiring a mining skill of 150 or more.
The zones listed below are not really different from each other, you will usually get the same amount of Mithril no matter which one you choose.

Mithril Ore

Burning Steppes

Burning Steppes is a great place to mine Mithril. You will find a mountain called Deadmaul Rock, there are loads of Mithril Deposits inside the caves there, but you have to fight mobs and you will get dismounted if you go inside. I recommend just leave this place alone, there is plenty of Mithril at the corner of the map if you just follow the route I recommend.

Badlands

Badlands is pretty close to Burning Steppes, so if there is someone already farming there you can go to Badlands or if you level is not high enough to go to Burning Steppes. This zone has an easy and simple loop to follow.
I marked a cave with a red X on the map, only go there if your level is a lot higher than the mob's level in the cave. It's full of Mithril but there is a bunch of mobs there, so you will actually get less Mithril if you can't kill the mobs fast enough.

Felwood

The route in Felwood is really simple and easy to follow which makes this an excellent place for farming Mithril Ore, just run a big loop around the zone.
These are the best zones if you want to farm Mithril Ore

Thorium Ore farming

This Thorium Ore farming guide will list the places where I was able to farm the most amount of Thorium in the least amount of time. There are a two types of Thorium Veins you will encounter on these routes, small and rich. Rich Thorium Veins requires a mining skill of 215 while the Small ones requires 200. I would recommend to get your mining up to 215 before you start farming Thorium Ore.

Thorium Ore

Winterspring

I believe Winterspring is the best place for mining Thorium, there is so much Rich Thorium veins in this zone. You could actually just go off the route that I recommend and you will still find Thorium everywhere.

Un'Goro

The reason I like Un'Goro is because of the layout of the zone, one big loop around the zone and that's it. It's so easy to farm there.

Silithus

Silithus is also an excellent place to farm Thorium. There are bunch of caves filled with bugs, don't go inside them. If you go inside the caves you will have to fight mobs and you will get dismounted. You might also get lost in those caves because it is hard to find out.
These are the best zones if you want to farm Thorium Ore.

Fel Iron Ore farming

This Fel Iron Ore farming guide will show you the best place for mining Fel Iron Ore. You need a Mining skill of 275 if you want to farm Fel Iron Ore and you can only farm it at Outland.
You will notice that this ore is a lot less common than Thorium or any other ores in Azeroth, this is the reason why Fel Iron is usually expensive at the Auction House.

Fel Iron Ore

Hellfire Penninsula

Hellfire Penninsula is the best place where you can farm Fel Iron. The route below is the one that I think will give you the most ore. The respawn time is fast enough that you don't have to go around in the whole zone, but if you notice someone else farming in the zone, you might want to try just to go in a big loop near the edge of the mountains.

Zangarmarsh

Zangarmarsh is a good alternative to Hellfire Penninsula if it's heavily farmed by players. (usually it is)

Adamantite Ore Farming

This Adamantite Ore farming guide will show you the best places for mining Adamantite Ore. There are two types of Adamantite Deposit, one if them is the normal Adamantite Deposit and there is also Rich Adamantite Deposit. The normal requires mining 325, while Rich Adamantite Deposit requires 350. This means it is recomennded to have at least mining 350 before you go farm Adamantite Ore.
I must also mention that Khorium Veins are a rare spawn of Adamantite Deposits, much like Truesilver is a rare spawn of Mithril, so sometimes you will find a few Khorium too. A mining skill level of 375 is required to mine Khorium veins.

Adamantite Ore

Nagrand

Nagrand is the best place to farm Adamantite Ore. I marked a few caves with a red X on the map. You can usually find one or two Adamantite Deposits in those caves so you should go into them.

Netherstorm

Netherstrom is also an excellent place to farm Adamantite Ore. Just like in Nagrand, I marked two caves with a red X on the map.