My concrete driveway slopes down toward the house and levels out about 3 feet from the house. From the house it slopes very little toward this same spot. During heavy rains the water collects in this spot and comes in under my garage door. What is the best way to prevent this from happening without spending a fortune?

A slot drain is the only thing that comes to mind without knowing a lot more detail. A slot drain is basically a pipe with an open top that can receive water and carry it away, provided that there is a location to outlet it.
Only other thought would be a berm across driveway (if asphalt driveway-or concrete possibly) which of course will create a bump.
If not a paved driveway (just noted that it is concrete but leaving this suggestion here as still a slight possibility dependent on whether basic driveway structure could still be possible?), one other inexpensive but probably short-term method would be to install a stone (golf ball sized stone-say) trench across the dway on an angle to intercept and carry the water away-but with all the above suggestions the grade must be such that the water can flow with a slope away from the problem area.