What can I do with...
 

The ripped of sleeves of a denim jacket?
I don't want to throw them away because that'd just be a waste.
Make patches?
Or any other ideas?

I dunno what the hell you're gunna do with those....unless you sew random rips of denim onto...I dunno......no don't do that.

patches it is then!

Make a purse? Or maybe stitch them onto the back of a pair of black pants and make pockets? ? I do not know, sadly.

Stitch them onto a t-shirt to make a long-sleeved shirt and pretend that it was a post-modern fashion idea from the outset?

It isn't quite the same but when I made cutoffs out of one of my favorite pairs of jeans I made the bottoms into a skirt (lined with some black fabric as I did not want my ass showing) with matching arm warmers and the rest of the scraps are going to be used for a patchwork denim vest as soon as one of my other pairs of jeans require surgery (I love them best as pants but when the knees are hanging on by the inside seem alone then they are best used for something else)

I think patches is the best idea.
I'll layer them with another fabric.
So it doesn't look horribley plain.

Yes I sometimes make patches with left over bits of jeans.