Truly the best in offensive weaponry, the Ultimate Weapons can make mincemeat out of even the strongest opponent (like there are any :)).

Ultimate weapons have zero Materia growth, but have eight holders, and every two holders are linked. When using the 'Morph' materia, the amount of damage inflicted drops to 1/8th, but with an Ultimate Weapon, the amount only drops to 1/3rd. There are also special ways to increase the amount of damage these weapons do.

The only exception is Aeris' Ultimate Weapon, which has seven holders and can gain AP. The Ultimate Weapons are:

Cloud Strife's 'Ultima Weapon':

Kill the Ultimate Weapon during Disc 2 or 3 to get the Ultima Weapon. This weapon does damage based on the (lack of) difference between Cloud's current HP and maximum HP. In other words, the fuller your life is, the more damage you do. Note that this isn't similar to the way the Atma Weapon worked in FF3.

Barret Wallace's 'Missing Score':

Stick Barett in your party while climbing up the stairs to the Mako Cannon during the raid on Midgar during Disc 2. If Barett's in your party, a chest will be visible on one of the landings that contains his Ultimate Weapon. To empower Barett's weapon, attach materia to it that have lots of AP (such as mastered materia).

Tifa Lockheart's 'Premium Heart':

Get the Sector 5 Key and return to Midgar during Disc 2 or 3. Go to the Wall Market and enter the building labled "Item". Examine the computer and you'll get her weapon. During a battle, Tifa's weapon does more damage the closer she gets to maxing her Limit Break. If she does a Limit Break and misses one of the slots, the weapon's power will momentarily increase, then lessen.

Aeris Gainsborough's 'Princess Guard':

While exploring the Ancient Temple during Disc 1, open the chest in one of the corridors connected to the clock puzzle room in order to get the Princess Guard. If her allies are in critical condition or are killed, the power of her weapon shoots up.

Red XIII's 'Limited Moon':

Prior to the raid on Midgar City in Disc 2, or during any time in Disc 3, go to Cosmo Canyon with Red XIII in you party. Bugen Hagen will give him his Ultimate Weapon before dying. The Limited Moon does more damage depending on how much current MP Red has, just like how the Ultima Weapon's ability to inflict damage depends on Cloud's current HP to maximum HP.

Yuffie Kisaragi's 'Conformer':

Her Ultimate Weapon is found in one of the chests in the wrecked Shinra plane that's lying on the sea floor. When fighting enemies, if they are of a level higher than Yuffie's, she does more damage per hit.

Cait Sith's 'HP Shout':

Found in the back row of lockers on Floor 64 of the Shinra HQ, during the raid on Midgar City in Disc 2. Just like the Ultima Weapon, Cait does more damage depending on how close his current HP is to his maximum HP.

Vincent Valentine's 'Death Penalty':

Put Vincent in your party and visit Lucresia during Disc 2 or 3; she's in the Waterfall Cavern on the Western Continent and you can get there using a Green Chocobo or the submarine. You should go here as soon as you're able to. Then, visit Lucresia again at a later point, and you'll find the Death Penalty and his Chaos Manual lying in the cavern. The Death Penalty's power raises in proportion to how many enemies Vincent has killed since joining your group.

Cid Highwind's 'Venus Gospel':

After the Rocket Huge Materia Quest, return to Rocket Town. Talk to the old man who gave Cloud the Yukiyoshi. Chat with him repeatedly and he'll produce the Venus Gospel for Cid. Like Red's Limited Moon, the amount of damage this weapon does depends on how close Cid's current MP is to his maximum MP.