Nikkor 28-80mm 1:3.3-5.6 G lens?

I have an old NIkon F55 with a NIKKOR 28-50mm lens. Would it work with a Nikon D3100?

It will work but it won't autofocus. Only AF-I (rather obscure) and AF-S lenses will autofocus with a D3100, or their third party manufacturer counterparts. That lens however is an AF one, not AF-S.

It's a pity - i have that lens myself and like it quite a lot on my D90 (where it autofocuses). I've found it to be nice for closeups, as its good close focus limit (for a non-macro lens) combined with the crop sensor gives a decent reproduction ratio. Despite of being a cheap kit lens, i've found it to be optically quite good - perhaps because a crop frame camera crops out of the sweet spot in the middle.

It's not a lens that i'd chose a different camera over though, the D3100 is nice. If you can spare the extra change for a D90 and don't care about video, then that'd be a good idea though, and you might save the extra price again by being able to use the cheaper 50mm/1.8D instead of the $200 more expensive 50mm/1.4G if you want to get into portraiture.