Though labor intensive, an asphalt drive goes down much faster than concrete, making it much less expensive to install. Before installing a new asphalt drive, be sure it has a good clay base and is properly graded and compacted so it will drain well.
Here's how to repair and seal cracks in a concrete slab, such as a driveway, to prevent water from seeping beneath the slab and causing the soil to erode.
Nice video about asphalt driveway installation.