As with the socks, I am posting links only to patterns I have actually made. If there is a baby hat you love and make all the time, please do post the link! (Crocheters, you too -- I am a relatively inexperienced crocheter so don't have a whole lot of experience there, although I do plan to try a crocheted hat pattern this weekend.)
You can, of course, use any pattern you like. This is just meant to be a short list of a few simple hats for those who do not have a pattern.
This mock cable baby hat (worsted weight) is fun, and the cables act like ribbing to pull it in, so it fits for several months.
This hat (worsted) can be made with or without the earflaps.
This very basic hat (worsted) is quick and simple.
Make only the larger (13-inch) size of this sock yarn hat; preemie hats are not needed.
My recipe for a simple rollbrim hat made with sock yarn follows. The 96-stitch version comes out to about 13 inches around; the 104-stitch version is closer to 14.
1 50-g ball of sock yarn (200-230 yds)
double-pointed needles of size you need to get gauge of 7.5 sts/inch (30 sts/10 cm)
Cast on 96 (104) stitches. Join in the round, being careful not to twist.
Work in stockinette (knit every round) until work measures 5.5 inches from cast-on edge.
Begin crown decreases:
set-up round: *k 12 (13), place marker,* repeat from * to * until back to beginning of round. Use a marker of different style or color to indicate beginning of round.
Round 1: *knit to 2 stitches before marker, k2 tog,* repeat from * to *
Round 2: knit every stitch
Repeat rounds 1 and 2 until 48 (56) stitches remain.
Now work round 1 every round until 8 stitches remain.
Break yarn, leaving a tail of 8-10 inches. Thread through 8 remaining stitches, pull through to inside, and weave in ends.
Remember, use yarn that is at least 75% wool or other animal fiber. Some of these patterns recommend acrylic, but that's not acceptable for the A4A baby shower.