I think there's a high probability that one's answer will depend on how many different headphones they've heard. I'll concentrate my answer on what needs the headphone in question satisfies rather than the specific model I choose.
If I could only have one headphone, I'd want something with my preferred sound signature (slightly brighter than neutral) and which maximizes sonic potential (meaning most likely open-backed circumaural, as other designs introduce compromises). My current example is a DT880. If I heard something that fit my preferences better, I'd change to that. Basically I want extended, open, airy, neutral, and with a high enough impedance that source matching issues are kept to a minimum.
If I could only have two headphones, I'd want whichever one I selected above, plus a closed-back circumaural (one step down the sonic potential ladder, IMO). My SRH440 currently fulfills that role, but of course if I found something I liked better I'd switch to that. I want a little more bass and a bit less treble from my second headphone because it's the one I plan to use portably--I think that signature works better for portable use as it allows me to gently increase the volume (without fatigue from the treble) and compensates a little bit for how bass seems to get lost in noisy surroundings. I also need this headphone to be more efficient so low-powered portable players and general-purpose audio outputs (e.g. a computer) can run it unamped to decent volume.
Essentially, headphone #1 is my critical listening vehicle, whereas headphone #2 is more practical and has slight sonic deviations from #1 chosen to compensate for the environments in which #2 is likely to be used. Incidentally, apart from its journey from Bozeman, MT, my DT880 has never been outside my house since I purchased it in 2010.