On the exterior, cinder block walls in a basement touch dirt. Though the cinder is strong, it's also a porous material, meaning that water can seep through, especially during the rainy season. Fixing the problem can be troublesome because a complete fix will require you to excavate the area around the exterior wall. But you may be able to eliminate the water coming through the cinder block walls without taking such drastic measures.
Put on gloves and eye protection.
Repair any cracks in the cinder blocks. It's common for cinder blocks to wear out and crack over time. This allows even more water to come through. Fill these cracks with an epoxy. Mix and use the material according to manufacturer's instructions.
Paint the interior walls with a masonry waterproofer. This should be specially made to adhere to cement walls. A waterproofer will prevent water from coming into your home, though it won't necessarily stop the water from soaking into the cinder blocks from the exterior.
Divert water away from your home. If your land slopes toward your home, you'll have a hard time controlling water. Change your landscaping so that it slopes out, install a French drain in your yard or take other measures to divert the water away from your home.
Excavate the land around your exterior basement walls and waterproof the area with foundation insulation. The original construction probably did include this waterproof barrier, but it can wear down over a period of 25 years.