Jersey pocket, almost every mile of the distance that you can see in my sig. No ziploc bag or anything. Sweat has never been a problem. I had iPhone about 90% of the time and, after it died, I got Motorola Razr i (the one with the Intel chip.) Wouldn't leave home without it. I think I actually lost some fitness a couple of months ago because I couldn't train properly between phones (iPhone was already dead, I didn't have the Razr yet, and I didn't want to go more than a few miles from home without a phone.)

Instead of headphones with their annoying wires, I use LG HBS700 Bluetooth headset. Quite an ingenious contraption, surprisingly good sound quality for earbuds, it stays in place even at 40 mph, and it's easy to forget that you have it on if the earbuds are not in your ears. It's supported by Spotify and Audible apps.