Water ending up in a basement may be coming from roof runoff a few feet around the house. Improving drainage can greatly reduce the amount of water in the basement. Make sure all leaders and gutters are clean and functioning. Attach long pieces of downspout to the ends of your leaders to make sure water coming off of the roof is being deposited far from the house, 10 or more feet if possible.
There are commercially available paints for garage and basement floors that can help reduce the amount of water that comes up through the floor or out of the walls. These paints will not seal the concrete and entirely solve the problem, but if a small amount of water from time to time is the biggest issue, applying a layer of waterproofing material is a first step toward stopping basement leaks.
Breaking the concrete in your basement at the lowest point in the floor and placing a pump beneath the concrete to remove water can help stave off an oncoming flood during periods of high rain. It can also be used to reduce the amount of water in the basement after water is already present. Use a pump that can move at least 1,000 gallons an hour and run the outlet hose out a basement window and as far from the house as you can.
Sump pumps are installed beneath a basement floor and are triggered when the water table reaches a certain level. The water is then pumped out a drain to the street or into your main sewer drain in areas where that is not in violation of code. A properly installed sump pump can stave off all but the worst floods and can pay for itself in money saved.