This stuff is so darned useful I can't help but post this on the web.
I hate most deodorants and antiperspirants due to cost and efficacy and aluminum concerns (even natural rock crystal deodorant contains aluminum compounds, though they say it's safe).
I experimented around and finally found something that works, and according to the web, others have found it works, too, even on tough cases.
Just go to the kitchen and get out the box of baking soda (sodium bicarbonate) ... do not confuse with baking powder (baking powder contains baking soda plus a powderized acid, which makes it fizz when wet). You can put about an eighth of a teaspoonful of baking soda in your palm (you'll need more in certain types of water - up to a teaspoon). Add about a quarter teaspoonful of water, enough to get it wet (or more, if you had to use more for your type of water). Dissolve the baking soda into the water - the liquid should feel slippery, since sodium bicarbonate is a base. Apply directly to skin. Then go have a normal active day. Adjust quantities as necessary - you may need less, you may need more.
(Regarding different types of water: if your water easily rinses away the "slimy" feel of sodium bicarbonate, you'll need to use more. If your water does not easily rinse it away, you'll need less.)
Anyway, I don't touch the commercial deodorants or anti-perspirants any more. I don't need to. Thank God, and I meant that!
Note: too much sodium bicarbonate will cause some skin irritation. It also needs to be dissolved sufficiently, because dry powdery baking soda can chafe skin just like sand (though some people on the Internet just apply like a powder, so I guess they don't have problems). You probably really don't need much at all, just enough to cover the skin. Another note: the water solution will leave white stains on clothes or countertops wherever it drips and dries out, but it washes away easily. After all, one use of baking soda is as a cleanser!
Oh, and if you wake up with an icky tasting mouth (like if you forgot to brush your teeth), try a quarter of a teaspoonful of baking soda dissolved in a small quantity of water as a mouth rinse. Mouth bacteria like to produce an acidic environment, but baking soda neutralizes the acids very quickly.
Likewise, when I get acid reflux, I like ingesting a small sprinkle of baking soda periodically. This helps my esophagus stay pH neutral, and meanwhile doesn't make my stomach think it needs to produce a lot more acid. Sad to say, though, my best cure for acid reflux is avoiding chocolate....