We don't expect our employees in my organization to clean their offices/workspace, but we expect them to keep them tidy.  We employ a support services company which suppies our reception and security services, and also cleans our office spaces, meeting rooms, clears up after meetings and loads our dishwasher etc.  

Every so often (about once a quarter) we have Big Clear Out and, if needed, we hire a skip to take away rubbish.  We have a very efficient recyclying company that takes away waste paper for recycling.

With regard to general tidiness etc, I think it is helpful to get everyone to participate in developing a policy.  That way they have ownership of it.  Our offices are very pleasant, although not luxurious, and I think that having an attractive environment to begin with encourages people to keep it that way.  

The reward scheme we have is: not being nagged.

Hope this helps.

Raindance