While I do love Bahamut (although some of the variations on him are awful), Ifrit, Cactuar and ChocoMog, my favourite summon is Cerberus. This is probably not such an obvious or common choice, and it probably doesn’t help that his only appearance is in Final Fantasy VIII. I like Cerberus for a multitude of reasons.
First and foremost, he looks incredibly badass. This three headed beast has a look of raw destructive power similar to that of the most powerful dragons in the series. That perhaps makes his summon ability seem kind of a letdown when you consider it isn't a massive attack, but rather a buff. However, that buff - Triple and Double cast on all party members - is extremely helpful for either boosting your damage output or rescuing a dire situation. His junction abilities are also excellent and I never found myself wishing I had another Guardian Force on instead.
I’ll also note that most of my favourite summons are from Final Fantasy VIII – I feel that this game is where Square managed to perfect them to some extent. They were interactive, integrated, useful and varied. It had all the true staples of the series such as Ifrit, Shiva, Leviathan etc. while also adding a number of unique summons amongst the main Final Fantasy series such as Brothers, Moomba, Tonberry, Doom Train and of course Cerberus. I feel that Final Fantasy VIII is the game that put so little focus on summons compared to the likes of Final Fantasy VI, Final Fantasy IX and Final Fantasy X yet achieved so much more with them.
Oh, and it had a three headed hellhound named Cerberus. ‘nuff said.