My favorite used to be Soapwalla (original scent--the citrus scent was irritating), but that one has started irritating my armpits this year for some reason. I never smelled with it, and it didn't stain my clothes. I do have other skin issues going on, so my skin is more sensitive than usual.
I am currently using Primal Pit Paste in jasmine. I do think it yellows my clothes a bit. But I don't smell, and my pits seem to be happy again.
When my armpits are super sensitive, I use the crystal deodorant some others have mentioned. What I have found to be incredibly important with this one is to wash my armpits with soap before putting it on. Otherwise it doesn't work. I also sniff the crystal occasionally to make sure that it hasn't been contaminated with underarm bacteria. If it smells bad, then I rinse it off well and wipe it off, and it's good as new.
Along with the crystal deodorant, I put on some powder that I made from a natural body care recipes book. I think it has kaolin clay, cornstarch, and a bit of tea tree oil--can't remember. Anyway, I think that a dusting of powder on top of a true deodorant (where you will still be sweating) works really well. I have used talcum powder in the past, but some people are concerned about carcinogenic properties of talc. I did have a health professional some years ago tell me that it's a concern only if used by the genitals, but maybe that information has been updated since--not sure.