Um, we could call two completely different sound signatures "neutral" when it comes to headphones, and none of us would be right (or you could say "all" of us, if you're one of those "optimists" that I keep hearing about).
So, while I don't pretend to know what "neutral" is, my rating of various headphones on the warm/cold scale is:
HD600 - pretty near neutral as far as I can tell
K501 - cold
SR-404 - cold
K340 bass-light version - cold
ER-4P - yikes! very cold
UM2 - warm with recessed highs
E500 - warmish but a bit washed out
SR-001 - warm
HD650 - very warm, excessive bass and not enough highs (this is not always a bad thing)
So, now that we have some idea of what I consider warm or cold, here's what I like, by genre:
Classical - slightly warmish sound with lots of impact. Instrument separation and detail have to be good, and instrument tone and tembre have to be right, though I do prefer them to be a touch warm. HD600 sounds very nice here but it doesn't have enough detail or instrument separation.
Rock/Metal - warm and rich, with a big bloomy bass. The HD650 is very nice here on slower rock, and the SR-001 is very nice across the board. Rock is usually mixed to be thin and bright to sound better on average systems, and warm headphones take the edge off the sound and fill in the missing parts.
Electronica - cold and impactful, with as much detail and instrument separation as possible while keeping the highs smooth. The SR-404 is very, very nice here, though it has an annoying lower treble peak that ruins some songs. Ditto for the K340, it's even colder than the 404 but it's treble is more linear, making it sound smoother. A cold but lush system with psytrance or good chillout will completely blow your mind.
Jazz, pop, rap - I don't listen to them so I can't really tell you.