I've got a very specific strategy on what to do with cloth drops for my toons while I'm leveling them that I wanted to outline here. There are two things to consider first when deciding what to do with your cloth drops: is this the first toon that I'm leveling to 80, and is the toon that I'm leveling a healer.
If the toon that you're leveling is not a healer, you should definitely be leveling first aid skill while you're questing, so using cloth for first aid skills up should be your first priority.
For your first toon, any excess cloth other than linen (after first aid needs, if any), should be sent to a bank alt and stored. The reason that I suggest doing this is to use for reputation for your first level 80. One of the easiest way to speed leveling for later alts is to get the two BoA armor pieces for each subsequent alt - shoulders and chest. The shoulders are easily obtained by doing the Wintergrasp quests once a week (it will usually let you do them twice a week, actually, if you do them early enough on Tuesday or Wednesday). In order to get the BoA chest pieces, you're going to need the Crusader title, which means running about a month and a half worth of Argent Tournament dailies, but also being exalted with all of your factions home cities. And the easiest way to get to exalted, other than questing through each of the starter zones, is by doing the cloth turn in quests for each city. And that means wool, silk, mageweave and runecloth. So save it up, so that you're first level 80 can get to Crusader that much faster and equip all your later alts with BoA chest pieces for a nice 10% boost to xp.
After you've got one level 80 at Crusader, you could either work on getting a second level 80 there as well to make it that much easier to accumulate chest pieces for your alts, or barring that, I would just sell all excess cloth on the auction house.
Netherweave cloth and frostweave cloth can't be used for faction rep turn ins. If you've got a tailor and enchanter, I'd make Netherweave bags with all your excess Netherweave. Keep enough to stock out all your alts and bank slots and sell the rest. Frostweave can be used to craft gear which can be disenchanted, or can also be made into Frostweave bags, although these are significantly more expensive to make than the Netherweave variety.