A piece in the Guardian suggests making an old jumper into legwarmers.
There are other tricks you can try, too. I successfully cut up a large old sweater and converted the 'body' part into a knitted skirt - really quite simple with one big piece of elastic used for the waist.
If the arms have gone (quite often happens at the elbows), you have a tank top / gilet if you can carefully detach them.
Sweater 'bodies' also convert easily to knitted bags. Not really robust enough to use for carting your shopping around, but very useful for organising stuff at home. I have one for all my shoe brushes, polish, etc, and another that holds teatowels and dishwipes. (You could also make cushion covers.)
A rather specialised use for the arms, and also for old socks, is not going to be useful to many people. But if you play bagpipes, flute, whistle, or bassoon, a knitted instrument cover can be useful. At least you know your instrument is going to be nice and warm! I have a lovely set of bamboo flutes by Patrick Olwell and each of them now has a different knitted bag made out of an old jumper arm.
With hand knits (less so with machine knits) you can also unravel the garment and reuse the wool in your own knitting. However, it will be much more unruly than 'new' wool, often curling up in funny ways. Still, if you enjoy knitting, why not extend your stash of yarn rather than simply throw a garment away?