1995 Pontiac Grand Am Won't go in reverse

Try checking the linkage at the transmission. Sometimes the piece on thetrans. That the cable hooks to will slip a little

Yep, I have seen the gear shift cable go bad and cause this issue, here is how to replace it to help fix the problem.

ADJUSTMENTS
1. Apply parking brake and block wheels.
2. Position range selector into the NEUTRAL position.
3. Lift up range selector cable locking button.
4. Remove range selector cable end from transaxle range selector level, Fig. 5.
5. Position range selector lever into LOW position.
6. Position transaxle range selector lever into LOW position. Obtain LOW position by rotating transaxle range selector lever toward front of vehicle until it stops.
7. Snap range selector cable end onto transaxle range selector lever.
8. Press range selector cable locking button down into the locked position.
9. Position range selector lever into PARK position.
10. Remove wheel blocks and release parking brake.

Check out the images (below). Let us know what you find.