What are the flavor characteristics of under-roasted coffee? As a frequent coffee drinker, I can tell when the coffee beans have been over-roasted; the coffee is bitter.

What can I tell when the beans have been under-roasted?

What does under-roasted coffee taste like?
I suppose under-roasting and over-roasting are somewhat relative. I generally prefer a lighter roast (just after the completion of first crack) which might be under-roasted to some tastes. 

I've occasionally stopped a roast too early and then it's under-roasted to me (and I suspect anybody else) as well! In those cases, the coffee tastes sour and I don't mean acidic, but sour. The sourness is a little like the taste in bread that has got old and soured. It also has a taste that's reminiscent of tea. I like tea but not when when it's meant to be coffee! (If you've ever had Qishr - "tea" made from the dried coffee cherry husks - it's pretty close to that, which is not surprising I suppose.)
There are also other coffee tastes which are just absent from under-roasted coffee - there is simply less of that "coffee" taste (and it also disappears of the tongue very quickly) and the coffee also has less body.

If they are not too under-roasted, I find letting the beans rest a lot longer than normal can help a bit.