My mom had an 88' Corolla wagon for awhile, very nice car. She bought if for 350.00, it was a hell of a deal. The two problems we had were:
1. Water pumps, we replaced it, (MAJOR PITA) ran good for awhile, then after we sold it the lady who bought it said the pulley sheared off, then I guess it needed altogether replacing.
2. Exhaust systems, the first one broke, we welded it, then it totally fell apart from the cat-back. IIRC it was like only 150.00 for a new system.
Other than those it was an excellent car.