Keeping photos of one's newborn is very typical. Many parents even pay for professional photo shoots or have photo books printed of their baby's first moments.
There are many companies that provide newborn photography right in the hospital, such as Bella Baby and First Day Photo. Local photographers may also take newborn photos, and some provide cute props such as animals hats, blankets and letters to spell out the baby's name.
Some parents choose to have their photos printed into a bound book from a company such as Shutterfly, and some get them printed and put them into baby-themed photo albums.