Ok, I'll bite on this one, even if this does sound like a ploy to get women to say "ooh yea, that makes me hot!"
I am more likely to enjoy having my underarms tickled under the following conditions:
-I have recently shaved them and am not self-conscious about hair.
-The person tickling me is someone I am comfortable with and trust, bonus points for finding them attractive
-my arms are over my head (not wriggling fingers stuck between my arm and body, but stretched out)
-the tickling is soft, gentle, and teasing. Not intense, torturous, or sadistic
-feathers or soft brushes are probably also good
-if I'm not restrained, but can pull my arms down when I want to or can't resist anymore (bonus points if this is the game)
-the tickler is enjoying herself and enjoying the physical connection
In general, a comfortable and fun environment with someone I like is ideal.