Do you have grandparents, aunts, uncles, neighbors, anyone who lives further away to send them to? Might teach your child about "snail mail" process and it might be fun if they respond and he/she gets mail in return! :-)
As a kindergarten teacher, I would get MANY drawings from students. I hung them for a week or two and then took them down to make room for more. I usually recycled them...
But I like the idea of involving the child in the recycling process. That tells them that there isn't room to keep EVERYTHING (and will translate to toys, clothes, and other objects of theirs when you go through things before a rummage sale). They get to help decide what stays and what goes - it will tell you which projects THEY think were the most important. You could get a really cool project and want to keep it because it looks nice, or you could get a clay pile and they want to keep the clay pile because they had more fun and that was more meaningful to them. :-) Do they have a playroom? Hang them up in the wall in there and when you run out of space, then they have to decide which of their works they will take down in order to hang the new one up.
:-) Good luck! :-)