I listen to music (or podcasts or audiobooks) most of the time. (If there is another human being with me, I won't; I think it's a bit rude to have headphones when you're supposed to be enjoying each others' company.)

However, I never use earbuds. I use these, or something similar, which lets outside noise in and I can hear cars (and other things) around me. I know people will say that it's unsafe, but I'm still paying more attention to my surroundings than many peope who sort of "zone out" while running or cycling.