Let’s see if I can make this semi-brief. I’m a relentless basshead and have owned many dozens of headphones and IEMs with sub-bass being one of the most important elements I’m looking for.
My favorite sub-bass headphones are the JVC HA-DX1000 / DX2000. Their primary flaw (other than rarity) is that there are a couple of parts on the headband that are prone to cracking.
The JVC HA-SZ2000 has epic bass capability and some interesting tech, but sounds like you’re listening through a 1970s-era vacuum cleaner that’s been cleaning a crazy cat lady’s house for at least the past three decades.
Fostex makes several great sub-bass cans (TH900, THX00, basically anything based on the Foster design). Same goes for Denon (the ones that look exactly like Fostex woodies–same OEM).
Many of the open headphones with solid sub-bass are planars. Audeze makes some good examples. The LCD-2C has rather capable sub-bass and is about the least expensive viable open option.
Generally speaking, bigger is better. The larger the driver, the more bass-capable it’s likely to be (perhaps because it can move more air and flex more without distorting).
Sony has some big drivers in the XB1000, Z7, and MDR-Z1R, they just tend to be tuned like crap. I’d love a Z1R with a heavy dose of EQ, but I can’t justify owning such an expensive pair of headphones if I’m going to have to EQ it all the time.
Perhaps surprisingly, some of the most capable sub-bass headphones are actually IEMs. I tend to significantly prefer dynamic driver-based in-ears to balanced armature receivers both for the sound and bass impact.
Some of my personal favorites are the Future Sonics Spectrum G10 and Aurisonics Kicker/Fender FXA2 (same thing). My daily in-ears are the Future Sonics MG5HX (customs). Excellent sub-bass reproduction, outstanding isolation, and non-fatiguing tuning make for great bass-heavy listening all day at work.
There are quite a few more options if you’re willing to look at in-ear monitors. From inexpensive (Sony MDR-XB90EX, JVC HA-FXZ200) to offensively-priced (they shall not be mentioned!).
Other headphones worth a quick mention that I’m reminded of as I almost hit the “Reply” button: ZMF makes solid options as does MrSpeakers.
And one last thing: You must have a good amplifier to get the best bass quality. Bass suffers more than any other frequency from a mediocre amplifier or bad power.