Mageweave is very useful for tailors/enchanters, for they can create relatively valuable items to disenchant. For this reason, the competition for the best farming spot is usually pretty fierce. Be sure to implement Useful Farming Tip #1 (farm with your highest level character) if you want to actually farm anything.

Deadwood Furbolgs in southern Felwood are level 47-50 mobs and have a combined drop rate for Mageweave of over 100%, meaning that if you kill 100 of them, in the end you will have more than 100 Mageweave. This is pretty hard to beat, and is also well known.

Runecloth drops from Humanoid mobs level 50 and up, all the way to 61-62 in Outlands. There are several excellent farming spots in Azeroth and Outlands for Runecloth, and they are:

Silithus, The Twilight Cultists, Avengers, etc, seem to be made of the stuff. You can expect an aggregated drop rate of over 35% from these mobs.

Western and Eastern Plaguelands: All the Undead in both these areas have excellent drop rates for Runecloth, and make an excellent farming spot, since you're unlikely to run out of undead to kill.

Hellfire Peninsula. If you have the Burning Crusade Expansion Pack, you can farm Runecloth from Bleeding Hollow Peons (around coordinates 56,70). They reportedly have a 32% drop rate for Runecloth. The Unyielding Footmen, Knights and Sorcerers in the Expedition Armory (just south of Honor Hold) also have exceptionaly good Runecloth drop rates.

Netherweave: Pretty much all humanoids in the Outlands drop Netherweave, as it is -- for now -- the top of the list as far as cloth goes. The best drop rates are for level 70 and up mobs in Netherstorm, however there is one exception:

The Voidspawns resemble the Warlock's Voidwalker. They are not too tough to kill and can be found all round the huge diamond that dominates South Western Nagrand. The Voidspawns are in the 64-66 level range, and drop Netherweave at a combined rate of roughly 79%

When farming, whatever it is for, make sure your bags are empty. This goes especially around level 50 and up. The 'grey' vendor trash items you pick up will more than pay for your repairs and if you are lucky, will leave you a tidy profit on top of that.