Soap and water
Sometimes simple is best. Using a mild soap and a clean, soft cloth can get rid of those pesky prints. Make sure the cloth is clean otherwise you could cause scratches.
Again, use a soft, clean cloth so you don't leave scratches. Be prepared for vinegar to leave a smell for a short time, but it's a great alternative if you don't have a mild soap on hand.
Streak-free glass cleaner
Windex or another window cleaner will get rid of those prints easily.
A little oil polished onto the surface of your stainless steel can help prevent fingerprints after they have been removed. Remember to use a soft cloth and a little goes a long way.
How do you combat fingerprints? Let us know!