A good back story, good character design, as in how they look, move (Like in X onwards) and speak, how they fight in battle, their significance to the plot and, most importantly, how they tie all of these things together.

I cannot stress enough how good a character Tidus is. He may have been whiny, but it worked with regards to the game and nothing seemed out of character about him. If you had been taken from your world where you were a blitzball star and thrust into a world where you have a freaking monster like Sin and weird creatures like Hypellos, you'd be whiny too.

Squall (and the whole of VIII's cast, except for Seifer) was terrible. Instead of fleshing out a group of individual characters, they just used the typical high school setting and put the typical anime personalities on them. Squall's the troubled emo kid, Zell's the goofy loud mouth, Quistis (I always forget how to spell his name) is the serious type, Selphie's the annoying dittzy one, Irvine was the lady's man and Rinoa was just simply the persistent love interest. Seifer, as good a character as he was, is just simply the main character's rival. The whole (SPOILER)GF making them forget they were childhood friends gives the characters NO interesting backstory IMO.