If you follow Craftiness is Not Optional, then you've seen her "bapron" tutorial. I knew I wanted to make one for my sis-in-law who's due date was last week and is ready for that boy to arrive!
It's a bib, but it's sort of an apron at the same time. It covers more of their body/clothes from spills and ... my favorite part is that it ties in the back. My daughter pulls off her velcro ones mid-meal every day, so this would be a nice feature.
Make sure to check out the link to the tutorial so you have an idea of what it looks like on . . . it didn't really fit my 18 month old when I tried it on her, so make sure to check out the pics in the tutorial.