I really don't think the point is to keep scraps until you are so inundated and they take over your sewing room and/or house. Unless you really like scrap quilts, there is no point in making them. If you can't use the fabric, or you can't sew fast enough to use up all of your scraps, then I would suggest that you keep the scraps that you really like or can work with comfortably and pass on the rest.
As suggested above, there are many places to donate them: thrift stores, friends that like the scraps, senior centers where they quilt, guild meetings (even if you don't belong, they will take your scraps), and the like. You could even put an ad in Craig's List or the free Penny Saver and advertise your scraps. If you don't want them to come to your house, you can offer to meet them somewhere in a public area.
The main point is to keep something useable out of the garbage dump.