Yuffie and Barret are the best characters in the game imo. My party is always Cloud, Barret and Yuffie now.
People have already mentioned in this thread the reasons I like Barret and Yuffie the best story wise.
Combat wise, Barret and Yuffie are both Long Range badasses, meaning I can easily have an entire back row party for the vast majority of the game.
Also, my two favorite limits are Doom of the Living and Omnislash...lol Love firing both off right after each other (when a fight lasts long enough to do that), nothing like watching 2 characters go apes*** on the enemies one after the other...lol