What's the best headphones for listening to music on the computer and the iPhone?

Bose would be incredible.
I have the amazingly cheap and absolutely outstanding Sennheiser CX300 iPhone style (I think) they’re noise reducing, in ear head phones that I picked up for £30 ($60) and they fit in the iPhone’s crappy socket! BARGAIN!

Good suggestion from cage, perhaps consider going for a bit of a higher end Sennheiser (if it’s for a gift, which I’m guessing it is).

What form are you thinking of? Over ear, in ear… etc?

over the ear. And yes it’s a 2nd graduation gift for my son. That’s why I want to keep it under $200. He likes the kind that fits in back as opposed to on top of the head.

I have in-ear headphones made by Skullcandy. Eveyone I know has Skullcandy. I’m not sure what’s up with Skullcandy, but they work g-g-great for me :)

For reviews, try: http://www.head-fi.org

For shopping, try: http://www.audiocubes.com or http://www.ttvj.com

You can also do some research at: http://www.ilounge.com

I might add that headphones are a very subjective kind of purchase; you may want to consider a gift certificate for him, and let him decide. My research indicates that there are not too many high quality headphones that take that form factor (wrap around the neck); although, in-ear monitors (earbuds) and circumaural (over-the-ear) tend to be the prevailing choice for audiophile-quality monitoring.

Since you indicated that these would be a single pair for both iPhone and for computer, that may influence your decision somewhat. As an audio pro, I actually have separate pairs of headphones/earphones for various uses. I tend to use the earbuds for portable on-the-go use (gym, outdoor use), but at home in a controlled and seated environment,
I go with circumaural (over-the-ear). A good primer for headphone types can be found at wikipedia: http://en.wikipedia.org/wiki/Headphones

Lastly, these previous discussions had some responses that may be helpful:

http://www.fluther.com/disc/9112/good-iphone-headphones/
http://www.fluther.com/disc/11799/are-these-good-earbuds/

My personal recommendations for headphones for professional monitoring (I own and use all of these for pro audio use):
AKG 240 very flat response, used in recording and studio monitoring
Sennheiser HD595 great soundstage-almost hyper-real sound
Beyerdynamic DT770Pro very comfortable, and sweet spot for monitoring pop and hip-hop music
Grado SR-80 great sounding, though they are open-style-they leak sound on the outside (they are the lowest price, but equal in quality IMO).

In-ear canalphones/earbuds:
VModa Vibe and Vibe Duo compatible w/iPhone
Etymotic ER-6i and HF2 the HF2s also have the iPhone-compatible jack

Bose are the best!

sndfreQ is the best.

I like the headphones the iPhone comes with because they include a microphone built right in for talking on the phone via the headphones. That’s just me though.

@derektherock42: good point; the new V-Moda Vibe Duo and the Etymotic HF2s have the same feature as well, plus the same button that answers/ends the call, and pauses/advances the track when listening to the iPod.

I have the vmoda vibe duo that has the mic and can answer the iphone. They do some getting used to since they go in the ear canal. They work in my laptop and iPod shuffle as well.

I love Bose, but for the iPhone I use the buds it came with for the answering calls and track skipping feature. If Bose made something that you could use that feature it would be awesome.