Okay, a dry basement is possible. But it takes many steps to do so. First, when the home is built, it must have drain tile around the footer on the inside and outside. This collects the water and moves it away from the house or into a sump pit where a pump then removes it.
Second, the foundation must have a true waterproofing membrane put over it. Someone else mentioned a peel and stick product. These work, are expensive and are usually used on commercial jobs. Most homes use a polymer modified asphalt. This will stretch over cracks in a basement and keep it sealed. This is not "tar" or dampproofing.
To repair your situation, is the foundation block or concrete? Block foundations can be made waterproof by jackhammering around the perimeter, installing a draintile, and drilling holes into the bottom course of block. This will let water drain under the slab to the tile. You can find someone in your yellow pages under waterproofer to fix it. Just remeber to bring out your check book for it.
Finally, if you have a concrete foundation with a crack in it, you can inject a urethane foam into it. There is a
foundation crack repair kit here.