My favorite baby gift to give is a hooded towel. The ones found in stores are almost always made from stretch terry which isn't very absorbent. Everyone I've given one to has loved them. Here's a few links.
http://patchyapple.wordpress.com/200...hooded-towels/ I make them using this method for young babies. Rather than using binding I just serge the edges. I also machine embroider a cute design on the hood.
I've also made hooded towels for toddlers using this method.
http://www.butterick.com/bhc/pages/a...wels/towel.htm
I've used a hand towel for the hood rather than two waschcloths because it usually costs less than two washcloths. You could modify this idea and make it smaller for a new baby.
This is a pic of one I made recently. I stitched a strip of cute fabric on each edge of the towel and on the hood.