Places to start looking
Ravelry. At the moment, there are over 5600 Free knitting patterns for babies, and new ones are added frequently. Try this Ravelry search for free baby patterns. You can customize your search, but this will include all free ravelry patterns for baby, sorted by popularity.
Lion Brand Yarns. Lion Brand Yarn has a large database of free crochet and knitting patterns. It's a nice source of Easy and Beginner level baby patterns. Here's a link to the list of Lion Brand baby knitting patterns.
Spud & Chloe. Adorable patterns from Spud & Chloe. Check them out on their blog.
Pickles. Pickles is a Norwegian yarn distributor with lovely looking yarn. They also have a blog, where they give away very cute baby patterns. Here's a link to Babykit for Melker. For more patterns, check the left sidebar.
Berroco. Berroco yarns has a large selection of free pattern for babies and kids on their website.
Rowan. Rowan Yarns has a few free patterns for babies and kids, mostly for kids.
Purl Bee. Purl Bee, the blog for New York's Purl Soho, is a beautiful site. The patterns include helpful instructions and photographs. The Snuggle Sack is lovely. A great place to start is the Baby Project photo gallery, it's inspiring.
All Free Knitting. All free knitting collects links to free patterns on the web. It's a great source of free knitting patterns, here's the page for Baby knitting patterns.
Knitting Pattern Central. Another great repository of free pattern links. Here's the page for Babies.