CJ, there are some good sealers available that will help this problem, such as UGL Drylok. This is a paint-on material applied with brush and roller. Be sure to thoroughly clean the wall first to remove any loose material for the best results. A wire brush works well.
Particularly since you mention this seems to primarily be affecting one wall only, I would also look closely at the grade outside the home, especially on this wall. Is there adequate drainage to shed water away from the house? This is a very common problem and often the cause of costly damage to basements and foundations, yet correcting the drainage is usually the least expensive method of control and prevention. If your drainage is good, the Drylok-type sealants should solve your problem, but most important long-term is to be sure your drainage turns as much water as possible away from your basement walls to start with.