I know: the DARPA Grand Challenges are pretty close. Those problems are a bit isolated from reality though, for a number of reasons. There is little actuation, for example, besides locomotion. Real road conditions, such as bad weather, nighttime, traffic, etc., are not considered.
A set of every-day tasks to be performed by the same robot would be interesting. It would disallow custom solution to each individual problem. It would encourage common architecture and perception, e.g. 3D volumetric mapping and localization.
Here are some task ideas, some more difficult than others:
* Mop a floor with a traditional bucket, mop, faucet and cleaning solution.
* Delivery packages to the doorstep of a while block.
* Drive to that block and back -- across town
* Introduce yourself politely to everyone at a cocktail party.
* Go apple picking.
Interestingly, the solution could be partially tele-operated. No need for a fully autonomous solution if a cheaper tele-operated solution means "control centers" at remote locations. Think outsourcing the perception and cognition of a low-skill task.
Add any other ideas you like.