Seriously, you might consider shaving the pits. That really helps to cut down on odor. It's not really the sweat that smells but the bacteria that, well, eat the sweat. You see, armpit, groin, etc. sweat is higher in fat then general sweat and bacteria love this. By shaving the pits, you drastically decrease the surface area for bacteria to grow on and thus, greatly reduce odor. And getting anti-perspirant deodorant will help too.
However, there are those that say that anti-perspirants cause cancer (what doesn't nowadays?) and that's why women get breast cancer much more often than men. See, men usually don't shave their pits and much of the "cancer causing" anti-perspirants don't make it all the way to the skin of the male pit, while most women do shave. Of course, women also have much more breast tissue, estrogen is thought to promote cellular growth (and thus, cancer) etc., etc., etc.