Probably a combination of worn suspension components and poor alignment. Check everything and most likely you will find it's time to replace.
If it were me I would take the opportunity to upgrade with this setup (with greasable race bushings):
http://www.scandc.com/suspensions.htm#streetcomp2. Align it per their recommendation.
Then a set of bilsteins all around and replace the rebuild the rest of the suspension (antirollbar bushings, end links, etc.)
Also, check out your subframe to body bushings as those have probably never been replaced. If those are shot use
www.globalwest.net,
www.detroitspeed.com, or
www.speedtech-performance.com for interlocking
solid body bushings. And add subframe connectors.
For the rear, talk to Eaton or Hotchkis.
Finally if your rims are at least 7" wide, find a good set of 255/60R15s tires.
This combination should not only handle like a late model performance car, but improve the ride at the same time.