Baby socks and baby booties are cheap and cute and boy do babies ever go through them. Lost, soiled, gummed to death... okay, just kidding.

Another gift you might wish to include is a mobile for over the crib or bed. You could probably make it yourself if you wanted to.

These might be more helpful for the parents than for the baby, but I think that's okay. One year olds don't really get the whole Christmas thing.