Pretty much used everybody. My main party late in the game would consist of the heavy multihitters though: Tifa with seven Breaks and Cid with his Highwind. Combined with Cloud's Omnislash, there was very little competition from enemies... or the other characters.
If they had included a HP Damage Cap break, I probably would have used the other characters more often. But, Barret & Vincent's 7 attacks only have a couple of hits and I think I remember Yuffie and Nanaki's as being just one group hit. When you can just combine a magic spell with all, why would this limit break be useful?