Cloud - Omnislash, 15 hits at 3/4th base damage value. Note that all hits of Omnislash are automatic criticals, so it's nearer 1 1/2th base damage value.
Barret - Either Catastrophe (10 hits, 1 1/4th base damage) or Angermax (18 hits, 1/2th base damage). Statistically speaking Catastrophe does the most damage unless you're BDM is increased sufficiently with Hero Drinks to constitute 9999 damage at 1/2th base damage, or you are under the influence of Lucky Sevens after the initial wave of attacks
Tifa - All seven limits hit for a critical "Yeah!"
Aeris - N/A, though technically Fury Brand fills the limit breaks of the other characters
RedXIII - Either Stardust Ray (10 hits, 5/8ths base damage) or Earth Rave (5 hits, 1 7/8ths damage). Statistically speaking Earth Rave does more damage unless under the effect of sufficient Hero Drinks or Lucky Sevens
Yuffie - Doom of the Living (15 hits, 5/8th base damage). Note that with sufficient levelling it will do more damage than her Level 4 limit break due to the 9999 damage cap, although stastically speaking All Creation does more damage
Cait Sith - Dice at Level 60+ or Knights of the Round summon with slots at level 84+, both of which are random, unlikely events. Also of note is his instant death attack which bypasses all Death immunities.
Vincent - Splattercombo (5 hits, 1/2th base damage) or Satan Slam. Again Splattercombo will do more damage if Vincent is under the effect of enough Hero Drinks/Lucky Sevens
Cid - Highwind (18 hits, 11/16th damage).