If you're looking for a balanced sound in an entry-level audiophile set of headphones, these are the pair I have:
Shure SRH840
Amazon.com: Shure SRH840 Professional Monitoring Headphones (Black): Musical Instruments
For casual listening, they're a bit heavy, and not particularly attractive when worn.. But they work very well. I lucked out and got em on sale for about $160.
The Bose noise-canceling headphones that were mentioned in another post are very nice -- not as much from a sound quality perspective, but the active noise canceling is some of the best out there and they are VERY comfortable and light.
To answer the OP's original question I guess, stepping up to that price level ($200) gives you something which is overall better than a $12 pair of earbuds. And by "better", I mean that audio reproduction will be clearer and (often) more balanced (no distorted audio due to cheap drivers) and also the ability to reproduce a greater range of frequencies (highs and lows) audibly. Of course, the source matters too; good headphones won't make a 96k encoded MP3 sound any better. But for a decent to good source, better headphones allow you to hear a lot more than cheap ones would.
As a note, that price range is considered "entry-level" in terms of high quality headphones.
If anybody out there is interested in learning more, check out
head-fi.org. When I started doing research into headphones I was constantly visiting this site. There's a huge community of people there passionate about high-quality audio, along with other resources like gift guides, product reviews, etc.