For rock/blues/strings:
Grado SR325i
supra-aural
~$300
Forward sounding, slightly fatiguing, notoriously uncomfortable and sibilant unless paired with a warm sounding amp. These are not cans for accurate reproduction of sound, they are designed specifically for musicality. That said, in my opinion they are the most detailed and generally best-sounding headphones for under $500, maybe more. The bass response is not overwhelming, but is very tight and sharp on the attack. Words cannot express how wonderfully the drivers reproduce electric guitar, specifically the decay of notes. They have a 32 ohm impedance, so unlike many of their peers, these phones can be driven sufficiently by an mp3 player and still sound pretty good. However, they won't come close to revealing their true greatness unless paired with a decent amp.Top-notch build quality too.
For hiphop / electronic:
Ultimate Ears Super.Fi.5 EB
in-ear
~$200
These in-ear phones have a separate sub woofer...and wow. It goes without saying that purists who desire a flat response should stay far, far away, but if you listen to primarily bass-heavy music there really is no better choice for anywhere near the price of these. The bass is POWERFUL, but not boomy or sloppy by any means. Furthermore, these phones accomplish this without sacrificing definition in the high end. They are slightly less detailed than the regular Super.fi.5's, but not very much so. I strongly prefer them, but they are not ideal for classical or folk. Then again, I don't believe any in-ears are really suitable for classical due to the lack of soundscape.
For classical / folk / Jazz (depending) / movies
Sony MDR-V600
circumaural
~$100
These have a weak bass response, but their neutrality makes them particularly suitable for classical and folk. Not too colorful, some may find them boring. Still, they are accurate and reproduce acoustic strings very well. Above all, these are some of the most comfortable headphones I have ever worn, and so they are great for watching movies.