I just use the slips as assessment for learning - a quick glance at who 'gets it' and who doesn't. Sometimes we take them up as a class and I have them put in the correct answers, other times I just walk around and really quickly correct them, put on a sticker and send them home
I don't keep them around. Like you said, too much paper.
I have found that parents like having the exit slips come home because it gives them an idea of what's going on at school as well.