Headphones come in all different varieties. One can buy a pair of headphones
for one dollar in any 99-cent store in NYC. One can also easily pay over
$500 for a pair. I have probably owned 30 pairs of headphones in my life
and listened to many more. My assessment of the situation is as follows.
Some headphones go into your ear and some sit on your ear. The ones that go into your ear need to make a good seal with your ear hole if you want to get any bass. It has a lot to do with the correct match between your anatomy and the shape of the piece that goes in your ear. Personally, I dislike this type of system because I can never get consistent results. One ear always seems to be getting better sound than the other. And they tend to fall out when I'm moving. But if they fit your ear well, and I did once have a pair that fit my ears well, they can sound really good, particularly given their small size and light weight.
Other headphones go over your ear. These vary a lot in sound quality across the different models, but are not so much affected by the anatomy of the individual using them. The ones with small-diameter diaphragms usually have poor bass response. The ones with big diameters tend not to have spacious treble response. But if you are willing to pay $100 or more, you can get headphones with good treble and good bass.
I have a pair of Sennheiser HD-280 pros. They cost $100 at HeadRoom http://www.headphone.com. HeadRoom is an honest, knowledgeable online headphone store. (HeadRoom has only spammed me once in the months since they obtained my email address.) The HD-280s are large headphones. They have closed backs. This means that when you're wearing them you are in your own world with the music. But the sound quality of closed-back headphones is always worse than open-back headphones at the same price. The HD-280s do not have the sparkling detail of some open headphones that I have heard. And their bass is not as clean and tight as some other headphones, but they are still very satisfying. Let's put it this way, if the headphones that came with my MP3 player are "1" and the best headphones I've ever heard (Stax) are "10" then the Sennheiser HD-280s are around 8. Actually I think that my Grado SR-60s were better sounding and cheaper, but they were open, so it isn't fair to compare them.
If one doesn't care about keeping your music private and blocking outside sound, getting a pair of large open-back headphones is the best move. Great sound can be had for around $100. But the problem is that good headphones expose the bad sound quality of most MP3s. Fortunately most "MP3 players" can also play uncompressed files, which are much better sounding.
I have a pair of GK-Music Ultraphones. They have extremely good attenuation of outside sounds and are good sounding. They are comfortable, not heavy and don't squeeze my head. Needless to say, they are closed-back headphones. There is an interesting tradeoff. Being closed-back, they have a less transparent sound than good open back headphones, and would tend to transmit less detail. But the isolation they provide allows me to hear
Update (April 24, 2006): I have been listening to the GK-Music Ultraphones for hours every day for the past weeks. They are currently my favorite headphones. I actually find them more comfortable than the Sennheiser HD-280s and I prefer the sound of Ultraphones. The isolation of the Ultraphones makes listening a much richer experience. On one recording, I think I can actually hear the HVAC system in the studio where the music was recorded! Of course an increase in perceived detail can be also achieved by just turning up the volume on any decent pair of headphones, but then the sound will be tiring and will destroy your hearing. So, all things considered, I am a fan of the Ultraphones.