If the moisture is water seeping through the block walls, then there are 2 things you can do.
1. Divert water away from the foundation at the outside of the house. Depending on where you live and the terrain (slope of the land), you could put in a french drain and use gravity to divert the water.
2. Seal the block. You can buy block sealing products that contain portland cement. The cheeper products that sell for $35 per 5 gallon bucket work well. Block sealer works best over unpainted block. If you have serious leaks, you could try the better products like Dry Lock from UGL. This costs about $90 for 5 gallon bucket and contains more portland cement than the cheeper product.
In some flat & sandy areas of the world with the water tabel near the surface, you may need a sump pump to keep your basement dry.
Remember that it is better to divert water outside of the home than from the inside.
Also note from other posts that in some climates, moisture could be water vaper coming through the walls not water. Some amount of water vaper should be expected, and a dehumidifier like dave suggested is a good idea...