Running or cycling? Not a chance. iPod headphones will fall out of your ears within the first 100 feet. I've never seen anyone running with iPod headphones; just walkers or commuters on the subway.
Exercise headphones are "disposable" too. I'll go through a pair every 4-6 months because the speakers eventually get clogged up with junk from sweat and eventually get muffled out. Speaker wire connections get frayed too since they're moving around a lot.
Sony MDR-J11G headphones work well for me running and cycling. They're $10-15 each depending if you buy them on eBay or in a store.
Apple wants $29 for replacement headphones. Even if they were designed for sports as well as the MDR-J11G's, they'd still be a rip off at that price.