email chess
you COULD, though then everyone would need to fully understand algebraic notation, you can't replay through the game, the spam issues are a nightmare, email doesn't handle images that well (because of spam)...
I have played email chess at www.ewccf.com for a while now, and I like it a lot. But there are more sites, have a look at google. If you search for email chess or email correspondence chess you'll get quite a few hits.
what's the best site to do email chess?