I also have friends who say the thing about "if it's still ugly you haven't cut it small enough" but I've seen some pretty awful fabrics over the years!
I buy a lot of my fabric at thrift stores, often in big bags. I sort through and toss the non-quilting and otherwise hard to use small pieces. Larger pieces that aren't quilting suitable accumulate in a bag until I have enough to donate back to the thrift store.
I've been trying to reduce my stash and make it easier to deal with -- but always remember that beauty is in the eye of the beholder. Recently I sent some large pieces of yardage that I decided I was never ever going to use but I thought might make a nice rug like people are doing nowadays, the recipient thought it was great just the way it was.
I've been lucky enough to make some friends here on Quilting Board, one of who makes crumb quilts. I keep a flat-rate postage box by my cutting table and all the scraps from my fussy cutting and those less than the minimum size I want go into the box and off to her. I've decided that I don't really want to store anything smaller than 6.5" wide, and nothing shorter than a 6.5" square. Recently I filled an entire box with nothing but 2.5" strips and squares -- seems that size is always used but I just don't want to deal with them any more. I can always cut a 2.5" piece off of my 6.5" strips and they are easier to store and sort. I've tried different ways of organizing them, usually semi-color based but sometimes I'm just looking for florals, or non-florals, or civil war, or whatever it is it isn't the way they are organized.
String quilts or making fabric out of fabric is another way to use ugly fabrics. Again, cut it small and dilute the ugly with less ugly. A friend of mine was doing an ugly fabric challenge with her small group and was at a loss of what to do with it. We chatted a bit and she string pieced the ugly fabric into pieces big enough to make a tote bag and won the contest.