Your recommendations for cost-effective and musical sounding headphones?

It seems that Grado, Sennheiser, AKG, Audio Technica and Beyerdynamic are
most often cited.

I listened to my old "dreadnaught" Genesis' A Trick Of The Tail remastered through my recently acquired 225e phones today and, even though I've listened hundreds of times to this recording since it came out in 1976, I heard Hackett's guitar details as never before, plus Collins' melodic percussives. Quite the musical revelation. I've got about a hundred hours of continuous playtime on these by now and they continue to improve.

Great comments here. I need to hear HiFi Man and Audeze to get a sense of what alternate designs contribute to headphone listening. Recently bought a JDS O2 amp for my Senn Momentums and had no idea they could sound this good. Clearly amplification also makes a difference in perceived headphone quality.