Your basement is flooding because the soils around it either do not drain (are composed of clays, etc) and trap water against the foundation or because of a high water table. A good test would be whether or not you have dampness in there when it is not rainy. This would indicate a high water table leading to infiltration. It can also be a combination of both. Either way, infiltration is the result of hydrostatic pressure pushing the water in when the soils abutting your foundation are saturated, as well as the capillary effect of water being pulled into dry material (concrete or stone).
I'll give you three options from cheapest (and least effective) to most costly (and most effective).
1) Cheap - you can buy a sealcoating product at your hardware store. There are 'sealants' that dry clear, cementitious sealants that look like 'painted on' concrete, and elastomeric coatings that are rubbery and dry thick, black, and opaque. The latter are more expensive but do the best job. These materials create a vapor and liquid barrier to prevent water from entering. However, they are hard to get perfect, and if you do not get it just right, hydostatic pressure will find a way for the water to go in. They also fail over time, forcing you to spend money on maintenance. They work best in concert with a dehumidifer to remove airborne water vapor. Dehumidifiers are not a great solution, however. Creating an artificially 'dry' basement simply invites more water to come in (via the capillary effect).
2) Middle of the road: There are companies who will install a basement drainage system inside your home. What they do is cut in a 4" channel at the base of the foundation into the concrete floor. It runs all the way around and links to a sump pump that they install in a depression somewhere near the lowest point. The channel is filled with crushed stone, and when water infiltrates, the channel carries it to the sump which ejects it into your sewer or to the outside. This system is cheap to operate because it runs only in the presence of water. However, it still is allowing water to enter the home, which may lead to elevated humidity, and mold.
3) Best Solution (most costly). the best answer is to replace the soils around your foundation with a drainage system. An excavator will come in and remove the soil around your foundation. Once the soil has been removed, a vapor/liquid barrier is applied, usually the elastomeric type mentioned above. This prevents water from entering the concrete at all, helping to avoid infiltration. Next, the excavated soils are replaced with copious amounts of crushed stone which drains water very effectively. Before the stone is filled in, a 6" perforated pipe is placed at the bottom running all the way around the home to channel off the water that comes through the stone. The pipe then runs out to a location in your yard where it can daylight or tie into a french drain or leach field which must be installed. This is the cadillac solution and should work very well. It also is nice because no work needs to be done inside the home. However, the price tag is the highest, especially if you have poor soils in your yard and have to put in a leach field or french drain.