Who is your favorite version of the classic summons:
Chocobo: No preference.
Ramuh: No preference.
Shiva: FFX
Ifrit: FFVIII
Titan: No preference.
Leviathan: FFIX
Odin: Crisis Core probably has the most awesome animation for this guy, otherwise I'd say FFVIII.
Bahamut: FFIX. The story-releated Bahamut scenes were all totally epic.

Whose your favorite non-classic summon?
Gilgamesh.
Whose your favorite one time summon? (i.e. only appeared in one title)
Doomtrain or Anima. Can't pick.
Who is your favorite Ultimate summon? (Crusader, KotR, Eden, Ark, Magus Sisters, Zodiark...)
I'd normally say Eden... but after watching this, I'm leaning towards Ark.
Which game did you enjoy the summons the most in?
Battle-wise, FFX because of its unique summon-system. Story-wise, FFIX.