What is a good pair of headphones for my iPhone 3G that combines functionality, style and sound quality?

Personally, I love my q-jays. They sound awesome, come with a bunch of accessories (more than other companies), and are quite tiny.
http://www.jays.se/products.aspx?sub=qjays
iLounge gave them a solid A --
http://www.ilounge.com/index.php/reviews/entry/jays-q-jays-earphones/

I don't know about the iPhone specifically, but for my phone I use the Motorola SD HD for working out and listening to music. They are a bluetooth wireless set that also has a built in mic. They act as a hands-free set as well. So far they have been great.

V-Moda Vibes, just make sure you pick up the ones with the microphone.

A pair of wicked stylish, high quality ear buds would be the Nixon Wire iPhone w/mic earbuds. Built specifically for iPod, they're built with excellent materials and produce excellent sound quality. Fairly expensive, $90, but absolutely worth it. And a lot of people will comment on them because 85% of people have no clue about Nixon's headphones.

http://www.nixonnow.com/headphones/

Second vote for the V-Moda Vibe Duo. I got the V-Moda Vibes for my iPod nano- I was so impressed I had to get the Vibe Duos for my iPhone. Amazing sound quality, fantastic isolation, and they can stand up to sweat, rain, and they stay in my ears no matter what I'm doing. http://www.v-moda.com/collection/modaphones/vibe%20duo.aspx

You never mentioned your headphone preference, whether that be 'in ear monitors', 'supra-aural'(on ear), or 'circumaural'(around ear).

My personal recommendation, if you do not mind sacrificing some size for quality, are the AKG K81DJ headphones (supra-aural headphones). They are quite portable and are very easy to drive (meaning you won't need a headphone amp to give them juice, the iPhone will do just fine). If you are not quite an audiophile, but still appreciate high quality sound... then these are perfect entry level headphones with a very reasonable price ($57.99 + Free Shipping via Amazon's website).

WARNING*: The pictures displaying the above headphones make the headphones look much bigger than they really are. The headphones are actually quite portable and come with a carry pouch for travel.

If you're looking for in-ear headphones, try the apple in-ear ones (not the kind that come with your phone). They're like $80 and sounds way better than they cost. I used to have a pair of Bang and Olufsens that were crap and sounded like it. The Apple ones sound great, look great, and they have the Apple remote in-line which, obviously, works perfectly with your phone.

I like the beats by Dre. Both the cans and the in-ear versions are amazing. The cans will set you back 350 or more, but are a work of art for sure.

The in-ear set has a nice case and plenty of ear-fittings, plus the no-tangle ribbon cable works surprisingly well. Not to mention they are made by monster-cable, who are known for superior cable technology.

Reviewers may say that both of these products bias the lows in their sound signature, but I find them to be very well balanced.

I find the style of these products to be certainly up to par with the iphone too, so thats a plus.

It definitely has to be the V-Moda Vibe Duos. The sound quality is amazing, and they come with a microphone and play-back button similar to the one on the original Apple headphones. About $99.

Even though they are foldable, don't count out the Sennheiser PX100 headphones. They regularly get top honors as the best portable headphones under $100. They are often at Amazon for under $40. It also comes with a tight-fitting compact hard case. Search the 'net for reviews and you'll find that these are a great buy.