See this review for some examples: http://www.bit-tech.net/hardware/2009/02/13/replacement-ipho...
For the ones that don't, I'd also wager that the aftermarket community will offer an in-line adapter that adds the buttons capability to any set of standard headphones/earphones.
You just can't put your own bigger headphones and use the Shuffle properly. Suppose you break the earbuds, you must buy some new ones to Apple to skip the tracks !
It's not the quality I expect from Apple products, just a "buy and dispose" thing.
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.