If the selvedge edge is a good sturdy one and it's a long enough piece (say at least 3" or so) I cut it down to about 3/4" wide and save it in a jar to use as a ribbon. I love using these "ribbons" to tie up handmade gifts, and they come in useful for all sorts of things.
I just used one this weekend - my oldest dog gets "hot spots" each spring so we have a cone we have to put on her until they pass; I used one of my longer selvedge "ribbons" to tie the cone to her collar.
Shorter selvedges, if they're at least a couple inches wide, I'll use in a crazy quilt.