I will attepmt to use one from each game I have played.
Leader/Fighter - Cloud (VII). Natural leader and one of the most powerful and developed characters ever.
Heroine/Black Mage - Terra (VI). Celes is a good heroine too, but she gets beat out because Terra is a half Esper and has cooler hair.
White Mage/Summoner - Yuna (X). This is pre X-2 Yuna, where she could heal or call upon a powerful beast to do her bidding. How can you top that?
Master Swordsman - Orlandu (Tactics). He beats out Auron because his attacks are super powerful combined with his natural strength and the speed added by Excalibur.
Dragoon - Kain (IV). Not much variety, but do not underestimate the Jump. It can easily get you out of a sticky situation.
Blue Mage - Quina (IX). Frog Drop is awesome and Quina is the best character from this game. You have problem?
Annoying girl - Selphie (VIII). Yes she is annoying but her limit is one of the best ever. Full Cure gets you out of a jam quickly and the more elusive The End does it even better.
Ninja - Ninja (I). The Ninja can use haste! That was so cool. Plus he gets good armor and weaponry to go with his high speed making him a valuable speed threat.
Monk - Josef (II). I wish you had him for more than one dungeon. He finaly gets justice being among these elite members.
Thief - Faris (V). Rikku from X-2 seems obvious for this role but I hate Rikku. Faris is the coolest of the V chracters and is right at home in the Thief class.
'Dark' Character - Paine (X-2). Every game needs the mysterious dark character, plus she can be a Dark Knight which makes it work out nicely.