Is there a such thing ...

It all depends on your definition of "unpaved trail"

Do you mean it's nice, wide, and reasonably well maintained like a paved trail, just it's instead lined with dirt or gravel instead of ashphalt; or do you mean something like twisty singletrack through the woods?

A decently equipped hybrid should be able to handle the former without much of a problem, though you wouldn't really want to take a hybrid through the latter.

Whizard said:

... as a road/hybrid bike that will not be damaged on unpaved trails?

I'm shopping for a new bike to replace a cheap steel mountain bike, and would like to get something lighter and speedier, but I don't want to give up the fun challenge of dirt tracks. I've been advised by one bike shop employee that hybrids are not meant to be taken off paved trails. Is there such a bike that can do it all, or will I have to have two bikes?

Thanks in advance for any help y'all can provide.

Check out cyclocross "cross" bikes too. Designed to ride in rough conditions but with geometry more like standard road bikes than mountain bikes, and equiped with components that are meant to get muddy and still function. Not as hybrid as most hybrids if you like road bikes.

How about a good new mountain bike instead of your cheap old one?

Tim