Some good headphones
I'm a pretty big sweat-er and I routinely short out the switch on the white Apple headphones, which I otherwise like pretty well, if I use them working out.
Audio-Technica ATHCKP500BL. They list for $60 and sell on Amazon for $30 (same as the Apples). They sound a bit different than the Apple phones, but very good. The things I like about them are: (a) the design of the earpiece is very effective for keeping them in my ears; (b) the sound is more attractive than most $20-30 headphones; (c) they come with two sets of ear doc-hickies that let you seal out external sound better or let more outside sound in.
What you have to be aware of is that the right cord is much longer than the left one because they are designed to have the cord hang down on your left with the cable to the right ear going around behind your head. There is a short basic cable that extends to a (left) armband and an extension cord that gies you a more traditional length. I'm not sure how I feel about that but it works.
The do NOT have controllers, and thus won't short out there...but that's also a disadvantage of sorts. They are not designed for under water use, but they are designed to be hand washable in the sink, etc.
Hope someone else finds this helpful!