I have to agree with Shorty on being sentimental about the first few GFs you receive, however...

More so than having a specific favorite GF I have favorite pairings of party members and GFs. For example, I always put Ifrit on Zell because of their fiery attitudes, I always put Shiva with Squall because they're cold...etc etc. I remember on certain playthroughs junctioning GFs to people who's outfit was the closest color to theirs.

My favorite GF animation to watch is probably the brothers, which in text form looks something like *rock paper scissors sad face KABLAAM!!!!*

I'm also a big fan of Odin. Even though he comes in at random, I still wish there was a menu screen for him where you could learn some stats or get abilities from.