I know I do not need to tell parents to take a lot of pictures of the baby. It is just a normal part of becoming a parent and most of us have a camera nearby at all times. Movies of the baby are also important and as soon as a movie is filled, a copy should be made of it. Keep the original in a place that is secure and use the copy for watching.
If you are into scrapbooking, you may want to consider taking an extra photo of a certain event so that you can have one for your scrapbook but still have a photograph of the event for you regular photo album. The alternative to taking a couple of extra pictures is to just have double prints made. The extras that you don't use for your scrapbook pages can be given to the grandparents.
There are certain pictures that you may or may not think of snapping, but in years to come, you will wish that you had thought of doing it. The first thing that some families don't remember to do is to get pictures of the mom-to-be at various stages of the pregnancy. Take plenty of pictures at your baby shower, too, if one is given in your honor.
Pictures of the room that you will be turning into the nursery of the "before and after" variety are always fun and those work great for scrapbooks if you are beginning the book before the birth.
Photographs of baby's first few days and while still in the hospital are always a good idea. Not just of parents and baby, either. If the grandparents are allowed to hold the baby in the nursery it makes great pictures as well. Don't forget the picture of mom holding the newborn, and the same for dad and older siblings.
Be sure that as soon as you get the photographs into your hands (providing they are printed out even if digital) mark the date or event on back of the photograph. It is very frustrating in years to come to see a picture and try to remember the event only to turn it around to check the back and find blankness.
The day when you are able to bring the baby home from the hospital is another time to make sure to have the camera at the ready. Perhaps a shot of when baby is tucked securely into the car seat; also when you arrive at home.
Over the next couple of weeks, family and friends will be stopping by to meet the newest addition to your family. Don't forget to take pictures of baby's visitors ideally interacting with him or her. (Holding the baby, showing a gift they brought, standing over the bassinette, etc.)
As the weeks and months go by and then soon the years, there will be many "firsts" that you will want to photograph. These include things such as first smile, first steps, first tooth, first day of school, first Christmas, first birthday party, and countless other small and large milestones. Some things that might generally be overlooked are "fun" events such as first picnic, eating a first hamburger, first trip to church, baptism, and dozens of other things.
Have fun taking the pictures that documents baby's first years, and always have a working camera very close by.