Champions don't do too much, as said else where.  They could, however. 

Merchants could go on caravan route to increase their effectiveness.  It ties up Merchants, but at least it gives them a purpose.

Inventors can go exploring: and get a temporary research bonus based on every new tile or area that they explore.

Farmers could be used to harvest world-resources without the appropriate technology.  It would effectively kill off the farmer (just as it would the pioneer), but the benefit would certainly outweigh the death of an otherwise not useful class.  (20% is not that great of a bonus, considering most cities produce only 1 food per turn without a fishery...and then why would a farmer add to fisheries?)

Administrators could travel through foreign lands while unarmed, like diplomats (or more accurately, spies).

Adventurers could train troops: upgrading inferior units by a marginal amount.