Ok, here is my list:
1. Phoenix: Why? because phoenix summon is hard to acquire and the summon scene is so COOOOOOLLLLLLLLLL. Geezz, i just love it.
2. Doomtrain: yeah, one of the most favorites. watching it inflict doom and silence and zombie and vit 0 and so on never get bored.
3. Odin: simple because it's kind of surprise when seeing he jump in between the fights.
4. Gilgamesh: even more surprise when I cannot know what his next move is.
5. Bahamut: love his origins and his solid position through FF history.
6. Cerberus: help me get rid of junk spells in my inventory.
7. Diablos: Fantastic summon scene.
8. Carbuncle: make the fight with Edea in disk 1 a breeze.
9. Eden: long summoning time makes the boost ability have some place to use.
10-19: Alexander, Pandemona, Brothers, Shiva, Quazecolt, Ifrit, Cactuar , Tonberry, Leviathan, Siren: rarely use them in battles.