Mine is similar to blackmage_nuke's

Team 1: Hero's plus one party!
Terra, Celes, Locke, and Shadow.

It focuses on magic but has Locke and Shadow there to balance them out. High-end equipment like the Atma/Ultima weapon as well as Lightbringer/Illumina are used to make the team all around good. The team is about overwhelming power.

Team 2: We don't need smurfing magic!
Edgar, Sabin, Cyan, and Setzer

Focusing on abusing class abilites as well as some fun relic customization. The Figaro Bros. and Cyan do their thing while Setzer is fixed up with the Master Scroll/ Offering and Genji gloves with his Fix Dice to create a melee monster. A real fun party.

Team 3: The Unusual Suspects party!
Mog, Strago, Relm, and mystery member.

Using the more interesting characters, Mog with his Earth Dance is quite powerful in here, if you can get the Water Rondo to work he's even better. Strago's blue adds a bit diversity in magic and acts as a healer with White Wind and Mighty Guard. Relm is the parties main magic offense with her high magic stat. Her Control ability also eases more desperate battles. The last party member always changes.

Gogo, is basically a back up mage and with the Tool or Blitz command as a support skill he can round out the team.

Umaro, offers some much needed physical offense to the team. He's also just fun to watch when he does max damage by throwing moogles, children and senior citizen's into the enemies.

Gau, offers a lot of diversity and is very powerful but requires a keen knowledge of monsters and quick fingers to get him to the desired Rage ability (I never play on Wait mode). Probably the most broken choice. Gau is my usual choice for the Unusual team.