I use the first generation Sony Linkbuds. They are sort of like an open back earphone, as they have a hole in the middle that allows outside sound through. Since they are proper earphones, they sound significantly better than bone conduction models whilst offering the same safety and awareness benefits. You can also use them freely with any sunglasses or hat because they don't go outside of the ear.

I sweat quite a lot but have had no problems after 9 months of use. I've also used them in the rain - again, no issues. They are designed to be resistant against both of these with an IPX4 rating. They have also survived a few drops. Another feature I like is the ability to extend the touch control range out to your cheek bones, so instead of controlling them by attempting to tap the small earbud while running (and possibly dislodging them) you can just tap anywhere along the much larger surface area of your cheek.

The fit is the biggest problem for people and I had to try a few different combinations of the included wings before I found one that worked for my ear shape. That is probably what makes or breaks them for most - in every other aspect they are great.