I have often been called a basshead and more often perhaps been called more vulgar variants of that name.
I do pay more attention to bass than other people, but whereas a typical "basshead" may be satiated with excessive, bloated, slow and undetailed bass, I am not.
So, I would say "best bass" depends largely on what your definition of "best" here is.
The Beyerdynamic DT770 certainly has the largest amount of bass. It is tighter than most cans and still reveals the quality of the amplifier and source driving it. It also goes all the way down to 20hz or below. However, it's not the fastest or most articulate.
The Sennheiser HD600 is known by some as having good bass and some as having bass as a fault. The HD600 does improve dramatically with the use of a quality amplifier. However, even with the very best amplifiers, the bass has considerable rolloff in its deepest, a midbass bump that some people find enduring or even seductive and a gentle, soft quality. Some would call the HD600's bass relaxing. Less kind words would be fat and sloppy.
The Beyerdynamic DT931 is like a sister to the HD600 in many ways but the bass is very different. There is perhaps only slightly too little of it but what's there is very tight and usable. I would say that the quality of the bass is better than the HD600 but would expect many to disagree with me because we'd never achieve a standard definition for "quality" and in quantity, the phone is less than ideal.
I once owned a Beyerdynamic DT831 and sold it particularly because it was a little bright and such horribly rolled off bass. Much of the bass was simply missing. If you have a poor source or amp that cannot produce the lowest bass anyway, you may not notice this as much and what's there is tight and articulate like other Beyerdynamics but this is easily the phones' biggest weakness.
The AKG K501 seems to have a little more bass respresentation than the DT831 but it is likewise horribly understated. I have not had the pleasure of hearing the K501 on every amp but I have heard it on the Prehead, RKV and HeadRoom Max and have yet to hear this magic bass that appears under the right magical synergy and voodoo dance. Maybe I need an RA-1, a good battery and expensive interconnects.
The everlasting Sony MDR-V6 (aka MDR-7506) has very good usable bass down to the lowest lows but also has a bit too much midbass and is not very articulate and detailed. This is obviously a good DJ phone.
The Etymotic ER-4S strikes me as very flat and linear down to the lowest audible bass but is often criticized for its bass due to it obviously having very little "impact" in the way that not much air is actually moved. This is a shame because the audible bass that is present is very quick and lucid.
Electrostatics share much with the Etymotics. Also lacking in impact, they are in my view wrongfully accused of having too little bass. In my view the Stax SR-404 and SR-007 have excellent bass and are more revealing of bass texture and detail than even the Etymotic but physical air moved is of course very little.
Grados are well respected for their articulate and impactful bass and probably have an even better reputation because they seem to achieve it more easily with quality amplification--a combination of its design and impedance. The old HP-1000, however, does not seem to achieve so much of its potential without a very good amplifier. With a good amplifier, the HP-1000 has a beautiful clean, textured detailed bass with all of the slam anyone could wish for. It also seems to achieve that elusive "hardness" that the HD600 could never replicate and which Stax amplifiers seem to have trouble producing. I really don't have enough experience with other Grados to comment further but people who aren't bothered by their other flaws seem to have no complaint with bass performance.
