In high school and college I perpetually had this problem. Then I made two major changes:
1. Trimmed down my armpit hair. There's no need for insulation there anyways!
2. Switched to a non-antiperspirant deodorant. Turns out a lot of guys have a reaction to the aluminum in them which irritates the skin and creates [i]more[/i] sweat. Besides, aluminum might be implicated in a number of a long-term health issues.
These two changes and now I don't even bother...