How can I baby proof our hotel room when we travel?

Age dependent. The answer depends considerably on the infants age but in general protect your baby from electrical outlets, stairs, small particles on the floor, and from falls.
Porta-crib/playpen. Curious toddlers and mobile infants present a challenge to their parents when traveling. Using a portable crib as a playpen can help. Some parents bring along baby proofing supplies (electrical plugs/door knob covers/toilet latches, etc) many hotels will lock the in-room refrigerators for you. Watch for pinched fingers with drawers and doors. Moving furniture can block access to problem areas.
Inspect the room. When traveling with a baby or young child, the parents should inspect the hotel room carefully, looking behind the curtains, under the bed, etc . . .. Windows and doors should not be openable by a baby or young child. One parent should always be with the child. Be extra careful about water, as kids can drown in toilets or bathtubs.