How is "gone" pronounced?

English vowels have a large amount of variation between accents and individual speakers. Even among speakers who pronounce cot and caught differently, gone and on may be pronounced either way. Gone and on do not belong to any lexical set, but the closest one for me is cloth.

So it’s generally pronounced /gɑn/, and that’s the pronunciation I would prefer if you’re learning American English. But as you have noticed, in some accents it’s /gɔn/ (as in gaunt). As Peter Shor says, it usually rhymes with on.

I think /gʌn/ is possible, but would analyse it as an unrounded version of the /gɔn/ pronunciation, perhaps Scottish or northern English, in which gun is likely to be pronounced /gʊn/. And as with any vowel, in unstressed position it can become /ə/. So /gən/ is also possible, albeit unlikely because gone is rarely unstressed. For example:

He’s gone out to the store.
[ˌhiz.gən.ˈaʊʔ.tə.ðə.ˈstɔr]