I will actually check mixes sometimes on 3 different sets of headphones, and several different in-earphones.

I have two really inexpensive sets of cans; one from Samson that came with a USB mic in a package; and another cheap set from KOSS that are a bit bass-heavy. I have been using the KOSS for tracking as the isolation is pretty good with them.

As for in-earphones, I have several sets of custom fit and universal fit earphones from Westone, my former employer.

Mixes sound different on every single set of these. If I mix so that the offensive stuff disappears out of every one of them, I end up with a really weak mix. I do like to check how stuff that I've intentionally panned whether whole tracks or some effects, to see if the panning comes across in each. As the quality of phones goes up, I notice that the panning quality goes up as well - the whole stereo space seems to widen as there is more and more accuracy in the upper end.

I don't know if I could settle on just one pair.