Great Question!! We got our son started somewhere around his 3rd year picking up his own toys and cleaning his room. My 8 yr old daughter can clean her room, make her bed, sweep, clean the tub before & after she bathes, etc. It may sound extreme, but they have a daily routine that keeps us from having to do everything for them.
Giving them a few chores and responsibilities early on ensures that they take care of their things and are organized. They do not leave toys laying around everywhere and have the idea that we will do it for them. Planting seeds of responsibility early on is a key factor to the overall development of a child.
And it has to start early on to stick with them. When I was a kid, we cut grass, washed dishes, mopped, and had every chore under the sun. Now of course, we hated our chores but they served a purpose and instilled values that my brother and I carry today as men in our late 20's.
Our grandma had an old saying that " If they're old enough to talk, then they're old enough to understand! And If they can understand, they can do some chores!" Its funny how they are called chores for kids but responsibilities for the rest of us...! Awesome Question!