I like to give a basket of baby care supplies that you constantly need - wipes, bottle brushes, bath toys, bath soap, etc. It's not a personal gift by any means but helpful. When I was a new mom I appreciated having an extra bottle of baby soap or bottle brush in my closet because I felt like I always ran out or needed to replace them at the most inconvenient times.
I was so overwhelmed by all the baby clothes I received as gifts when mine were little! Baby clothes are the cutest, so I totally get it, but if I buy clothes (which I usually avoid) I stick with sleepers and sleep sacks.
All of my kids received such cute, personalized gifts when they were born. Picture frames, burp clothes, bathroom stool, blankets, stuffed animals, hand knit sweaters. After seeing such cute stuff, I decided to buy something personalized that will match the nursery colors for new parents.