You may want to keep a plastic trash bag in your car just in case your water breaks to put on the seat to protect it.  You may also want to carry maxi pads in your purse the last month of your pregnancy for the same reason.  Water breaking does not occur like in the movies (a sudden gush), but you may have a constant leak which can be unsettling.  For the same reasons listed above, you may want to place a plastic shower curtain liner on your bed.
 
Two cotton baby doll gowns (mid thigh that button down the front mid chest).  One gown to wear during the birth and one gown to wear the day after.  Mid thigh gives medical personnel easy access for exams and you as well to feel the baby's head.  Buttons down the front allows you to breastfeed easily.

Headband or ponytail holder to keep your hair out of your eyes and off your face.

Deodorant and body spray to freshen up easily and fast before visitors.

Massage oil (if you perfer aromatic ones, try to bring differing smells in case one becomes nauseating for you.)

Unopened bottle of olive oil, KY Gel, or astroglide for lubrication if you perfer their usage over hospital lubricants.

Socks for yourself.  Hospital rooms can get cold.

Maternity clothing for when you are discharged.  You will not have gone down significantly enough to wear pre-pregnancy clothing yet.

Your own medication you take regularly. 

Lanolin for nipples.  Breast pads.

Cell phone, names and phone numbers of people you plan to contact while at the hospital (supervisors in case unexpected delivery date and change in work plans, parents, extended family, friends, and clergy...)  Bring your cell phone charger!

Preemie outfit for your baby for the pictures at the hospital.

CD's and DVD's for passing time in the hospital room.  Try and take different types of music to fit differing moods. (Types of music for the atmosphere you want to create are ideal.  Soothing/Relaxing music for early/active/transition stage while upbeat for the pushing stage.)

Snacks as well as drinks.  Possibly something to toast with after the birth!

Camera and video camcorder (plus their chargers)

Baby journal - incase you would like to write a letter to your baby sometime at the hospital.   Which more than likely you will not have the time to do, but on the occasion, you may, and it is nice to have.

*Birth partner may want to bring a swimsuit so that they may join you in the bath or shower for some of the labor.

Things to take from the hospital:

Hospital bracelets (mom's, baby's, partners) for baby book, time capsule, and/or shadow box.

All the pampers in the room.

If you are bottle feeding.  All the formula in the room.

Extra nasal bulbs.

Sanitary pads and underwear.

Tucks pads

Reminders: 

1)     Have you made arrangements for your animals for when you will be gone?

2)     Have you made arrangements for child care of other siblings?