Our 350 sf. concrete walkway/driveway is cracked and broken and needs replacing. I'm considering replacing with either concrete, concrete pavers, or possibly asphalt. Are there other materials that could be used? What is the most economical solution?

Thanks,
Pete

Asphalt is the cheapest. Cement not far behind in cost. With the oil prices now everything is going way up.
Depending on a few factors will depend on what you should choose.
Area in which you live. If you have deep freezes asphalt may not be a good choice as it will heave and crack in short order.
Cement on the other hand can spall if a lot of salt is used on streets in your area so its sort of a toss up.
Pavers are a great method of doing a drive but are real expensive. So you have to be sure your area would warrant such an expensive upgrade.
Some folks mix and match. Using Pavers and cement.
There are several other methods of driveway systems all of which cost lots of cash and can be quite easily priced out of your housing market.
One utilizes a stone mixture with an epoxy to hold it together. It is used a lot around pools where standing water is not wanted, as it drains very well. and provides good traction but is soft on feet.
Think of what you had on the driveway for all the years you lived there. That may be your best choice when replacing it.