Sprites can be fun, and they can also make you wish to kill yourself. A long time ago, I found a pretty good starting tutorial (possibly linked from the old VERGE site, now that I think about it) that has sadly not been updated since December 2001. It's worth a look anyway, though, as it's good stuff, even if it doesn't focus solely on sprite art (it spends a fair bit of time on tiles as well).
Tsugumo's Pixel Art Tutorials