Ever try running with ear buds in? It doesn't always work out so good. Full headphones may work, but the headpiece can still slip and bobble around.
I'm lucky in that the main sport I use headphones for--snowboarding--has a seamless solution: the headphone beanie. The headphones stay put, cause no discomfort and deliver my tunes without a hitch.
Unfortunately, a beanie isn't exactly good for warm-weather sports like running, cycling or hiking. Which is why designer Bengamin Lotte came up with the Headbanger Headphone. Specifically for athletes, the headphones are essentially earpieces integrated into a sweatband. The adjustable, elastic headband conforms to your dome keeping the earphones right in place. And unlike my headphone beanie, the Headbanger 'phones are designed to work with larger, over-the-ear cans to deliver the biggest base and most accurate sound.
While these are just a concept, I'd be surprised if someone didn't manufacture something similar. In fact, I'm surprised someone hasn't already--these seem like a great solution for sports. Halo Headphones are close, but lack the bigger drivers of the Headbangers. Hopefully, someone will pick up where Lotte has left off...
EDITOR'S NOTE: These headphones are not available. These sports headphone and these sports headphones are options you may want to consider.