Good question! My children are still fairly young, but they clean up after themselves, put clothes in the laundry and tidy up messes they have helped to create. They like to vacuum and I let them do it, but because they are young they miss bits and I often have to do it after them. We have a movie night once a week, and the deal is that they clean up before they get to see the movies, then they get ice cream, popcorn and chocolates to eat while enjoying their movie. They love it because it's instant gratification and I love it because they're tidying up!
Our kids are part of the family team. So we all work together keeping the house in shape. They do things from cooking dinner to tidying their room. We all chip in and do our parts and chores vary daily!
My children (7 and 9) do general tidying, empty and load the dishwasher, sweep and vacuum, and that's mostly it. We've been gently increasing what they do as they get older, but not making a big deal about it - it's all part of being a family team.