All the uses I can think of for cloth (that may or may not be related to tapestries, which are a great idea) that don't include clothes:
1.) Tapestries (duh)
2.) Bedsheets & Blankets
3.) Curtains
4.) Cloth doors/Tents/Tarps (mentioned earlier in the thread)
5.) Pillows/cushions (for all those hard, stone chairs!)
6.) Banners/Flags (which are, admittedly, a lot like tapestries)
7.) Bandanges (I haven't checked the recent dev-notes to see if this is in the hospital stuff or not)
8.) Carpets and/or rugs mentioned earlier in the thread
9.) Furniture covers (for aesthetics, a little more Elven and Human, probably)
10.) Trap uses mentioned earlier in the thread.
... And that's all I can think of - and most of those were mentioned already. Would many of them be useful? Maybe not. I think adding bedsheets might make beds a bit too complicated, and adding bedsheets as an aesthetic (read: value) improvement would, again, be a bit of an ordeal. Would we then need cloth just to MAKE beds, or would we need to make bedsheets, then place them on beds ourselves? Do you really want to have to do that? (I kind of do, but hey...)
With squads and armies, though, flags & banners might be cool. I can't think of a game mechanic they'd have, though, except to force you to use flag carriers.
Other uses I see as primarily non-Dwarf. It's not very Dwarven to cover up that stout rock throne with a cushion, making it all soft and wimpy like some Human or Elf throne. It's not very Dwarven to make a tent, which would blow down easily (unless, of course, that Dwarf were on a very, very long expedition away from home. Like... on his way to a new outpost) and might look kind of Elven with its lack of rock and metal and general awesomeness (although, I can see it now: This is a masterwork Giant Cave Spider Silk tent. All craftsdwarfship is of the highest quality. It is decorated with dragon bone and menaces with spikes of obsidian. It is masterfully dyed with dimple dye. An image of Urist McCheeser is sewn into the tent with giant eagle leather. Urist is holding Cheese. The Cheese is being eaten by Urist.")
I wonder... if you use a tapestry to cover an engraving, would it replace the engraving's value? Would the mason become unhappy if it were a legendary engraving? After all, you would be hiding it from public view (which might make good for a poor engraving of Urist McCheeser eating cheese, but not so much for a grand engraving of magnificent battle). I realize that tapestries would be intended to go on unimprovable, constructed walls, but it would only make sense that you could put them on other walls, too, and then you get this kind of question.
... But I've always wanted tapestries, too. Not even just to hang on walls, but from the rooftops of a grand throne room, or over my arena, or in my barracks and entryway, or even mounted on posts between the statues lining my roads. What a grand impression a fortress can make, when its roads are lined with fine GCS silk tapestries depicting the greatest moments in its own - and its civilization's - history.
... And what a poor one it could make with pig tail tapestries depicting Urist McCheeser eating cheese.
Caravan Leader: "Wow, they must REALLY like cheese at this fortress! Look at all these tapestries of Dwarves eating cheese! We'll have to be sure to bring them loads of it on our next trip."