Most of the time when you find water in the basement it is the result of inadequate drainage from the roof of the house after a severe storm. Other causes include excess humidity and the seepage of ground water.
When your gutters are clogged with leaves, a heavy rain will pour water directly onto the foundation where it will seep through cracks. Your downspouts may be too small or clogged as well. You should clean your gutters at least twice a year and make sure that you have enough downspouts to handle the rain and that they carry the water away from the house. You may also want to check if the slope of your yard from the house to the street is sufficient to carry the rainwater away from the house.
If the problem is excess humidity, the easy solution is to install a dehumidifier to make certain that the air in your basement remains dry.
If the problem is ground water, you have a significant problem that may require calling in a professional. If you're looking to do-it-yourself, there is a procedure that involves using hydraulic cement to plug the holes and cracks in the basement walls and covering the walls with waterproof masonry cement. This procedure might or might not fix the problem. One way a professional will waterproof your basement is to dig the yard around it and insert a layer of waterproof clay.
If the water in your basement is severe enough that you have standing water, you may have to summon a professional to get rid of it. You can also rent a water vac and attempt to do it yourself. You should get rid of any wet furniture and other items that might collect mold. Make sure that any wooden floors or wall panels have not rotted and, if they have, replace them.