My children and I have come up with something we call Personal Pursuits for them to spend their time on after the official school and chore lists are checked off for the day. I sit down with each child at the beginning of the month and come up with a list of 3-4 interests they have that they will work on that month. These interests really vary based on age, gender, and just plain old changing interests. I try to help the child think of things that they are interested in learning, developing a talent, or just trying something new. I also try to limit the cost and level of my involvement required.
My younger children have enjoyed drawing books and videos (janbrett.com has some great drawing videos). All of the children have been interested in basic stitching projects from time to time. This activity does require a lesson or two from me, but after that I supply some fabric or plastic mesh and thread and let them practice. Other pursuits have been origami, bird watching, various cub scout activities, finger knitting, chess, computer programming, gardening, paper crafting, paper airplanes, various collections, cooking, baking (both of these require my help and supervision for the actual activity, but the cookbook browsing and ingredient shopping lists can be done alone), etc. Topics they have wanted to learn on their own have been The White House, army uniforms through the ages, outer space, bugs, reptiles, guinea pigs, etc.
I really do expect them to spend time on these personal pursuits each day, but am unconcerned with how "productive" the end result is. In other words, if they choose gardening and really do spend some time everyday puttering in the soil with some seeds and a trowel and hose, but only 1 seed ever sprouts, and nothing ever flowers or fruits, oh well. They still gained valuable experience from that exercise. I also allow frequent changes (every few weeks, not daily or weekly) as new pursuits spark their interest and old ones fade away.
Hope this helps.