It's likely a condition called hyperhydrosis, and it is pretty common. I asked my doc about what I could do for it. I lived in Houston at the time, and it was really bad, especially with the heat and humnidity. I was going through 2 or 3 undershirts a day to just maintain the appearance of staying dry. Anyway, the doc told me it was nothing to worry about, and he wrote a script for a topical liquid called Drysol. It's an aluminum based liquid that you apply once every week or two or as needed, and it really worked wonders. I know how much it sucks to be out in a bar or something trying to meet women and you have big, wet salty marks in your underarms. It really zaps your self confidence even if you don't realize it. Unfortunately it is perscription only stuff, so you need to go see the doc to get a script for it, unless you are pretty tight with a pharmicist or something. It won't do anything for areas where you don't apply it, but it will at least save your clothes, and keep your underarms dry. Also, when you get that stuff, it works even better if you trim up the bush under your arms. No need to shave it all out, just cut it shorter. It'll itch a bit for a day or two, but it's not bad. All that hair acts as insulation to keep the warmth going in that area.
Good luck.