Will tomatoes keep for longer if you keep the stalk in?
Removing the stem from a tomato opens up a hole where air, moisture, and bacteria can pass through. Keeping the stem in, or somehow sealing the "scar" from the stem, will prolong shelf life.

(Published in Cook's Illustrated - requires subscription - http://www.cooksillustrated.com/howto/detail.asp?docid=1173)