My typical class combos go like this:

1. Ninja/fighter. I know there is a parvir class, but fighter abilities are much better imo.

2. Redmage/elementalist. Double cast + debuffs = pro

3. Time mage/black mage. Great combo for the moogle class.

4. Black mage/white mage. Great combo for the no mou.

5. Assassin/sniper. Nothing like vanish for 3 turns then killing something in one shot.

6. Dragoon/defender. Dragoons are sick all by themselves, they have high hp and don't need magic. Defenders have 2 abilities that combo and can potentially take out a lot of units at once. Aura/Melt down. If you use your assassin/time mage to stop units, you can melt down with 100% chance to hit, and it usually one shots them. I have used it to take out 3 targets in one shot.

Then of course your unit gets auto raised and can be healed.