I've never used a rewards system but I'd get my daughter to do age-appropriate duties around the house from an early age. For example, even very little children can do some dusting, pick up their toys, dry the washing and water the plants. I always emphasised that, since everyone in our family lives together in one house, it's the duty of us all to keep it clean and tidy. Young children often see cleaning the house as a game and actually enjoy doing it. The only problem is that sometimes they don't do such a good job, so you might have to redo it later (preferably when they're not around to see)! The point is, to get them into a good habit...one that they'll follow the rest of their lives.
To make cleaning more fun for young children, you can also buy wonderful kids cleaning sets with brooms, dust-pans and other stuff. My daughter had some of these when she was little, and they were amongst her favourite toys.