For mom 
Nightgown or shirt to wear during labor if you don't feel comfortable in a gown provided by the hospital (they should be loose fitting or something that can be completely opened in the front)

Robe or bed jacket

Socks

Slippers

Nightgown and/or pajamas (if breastfeeding, then bring ones made for nursing)

2 - 4 bras (nursing bras if you plan to breastfeed)

3 - 6 pairs of underpants

Toiletries (toothbrush/toothpaste, soap, shampoo/conditioner, deodorant, lotion, comb/brush, lip balm/chap stick)

Elastic/Scrunchie or hair clip to pull hair back during labor

A photo or object to be used as a focal point during labor

Going home outfit (something comfortable/loose fitting)
Optional 
Lollipops or hard candy to keep your mouth moist during labor

An activity (such as pre-addressing birth announcements or crossword puzzles) or a book to keep busy during early labor

Your baby book - you can record your delivery details and first moments with your baby and the nurses can put your baby's hand and foot prints on the appropriate page while they are inked for the hospital records

Cord Blood Collection kit (if you decided to collect your baby's cord blood)

Makeup, lipstick, scented shower gel or body powder to make you feel better after labor

Eyeglasses or contact lenses (keep in mind that you can wear your eyeglasses during labor, but you must take out your contacts)

Watch

Address book

A few small gifts or one for all of the nurses that helped care for you

A small gift for the other children at home from the baby
For partner
Insurance information
Hospital preregistration information
Change of clothes and toiletries, if they're allowed to stay in the room
Optional
Things to be used during labor: soothing music, something to be used as a focal point, tennis ball, rolling pin or lotion for massage, watch, paper/pen, snacks
Book or magazine for reading
List of people and phone numbers to call
Camera/film (make sure it's preloaded and in good working condition before you go)
Camcorder and/or cassette recorder with tapes
For baby
T-shirt, socks, hat
Going home outfit
Bunting/jacket (depending on season)
Receiving blanket (and a heavier blanket if it's cold)
Car seat (Keep in mind that you can't leave the hospital without it)