Lots of good suggestions here, but few have mentioned books. It was only when one newborn grandchild was given a lovely selection of books by a friend, that I realised what a good idea it was. A mixture of titles suitable for babies and slightly older children makes a good gift, including some classics like Peter Rabbit and Roald Dahl.
From my experience (5 grandchildren in last 5 years) parents prefer to buy all the basic baby stuff, though money towards expenses is always appreciated. First babies get loads of soft toys and clothes from friends, many of which never get used.