If you want to make the game interesting for a barb, you really need to look at the individual barb's char.sheet and see what he's good at besides dealing/taking a lot of damage. Maybe the player has selected any particular skills he hasn't gotten much from yet? Can he track? Is there anything in his background you can use?
It's not easy to come up with much generic advice, really. All we know is that he's strong and fast. If that's all the player cares about (unfortunately, this is true sometimes...

), then there isn't much to go on. What level is this barb, by the way?
You could always give the chance to break stuff; maybe the party needs to get through an old door with a lock that's rusted or maybe even welded shut so the rogue can't pick the lock? Bend apart the bars of prison cell perhaps, or break some mighty chains holding a prisoner/treasure/whatever...
Other ways to let him utilize his strength is lifting a portcullis the party needs to pass or maybe raising/lowering a drawbridge across a moot?
The only other thing I
know he's got going for him is his speed. If the party doesn't yet have access to stuff like Fly and Teleport, you could always let him save the day simply by
running very fast. Perhaps there is a message or a batch of medisin or an antidote that needs to be delivered really quickly? Possibly over terrain unsuited for horses?
For now, that's pretty much all I can think of... Wish I knew more about the specific barb in question though!
