Zorn and Thorn

Zorn and Thorn are a pair of twin jesters who serve under Queen Brahne of Alexandria in Final Fantasy IX.  They are known for being both annoying and having an odd manner of speaking where they twist each other's words. They are first seen in the beginning of Disc 1 in Alexandria Castle, after just learning of Garnet's disappearance. From then on, they become a constant nuisance to your team, until you finally battle them and defeat them for good.
 
The initial battle against Zorn and Thorn occurs on Disc 2 back in Alexandria Castle.
HP: Zorn ~5,000; Thorn ~3,000
Drop/Reward: Nothing
Steal: Zorn - Stardust Rod, Partisan; Thorn - Mythril Armlet, Mythril Armor
 Like most battles, you'll want to have Zidane use Steal often, mostly on Zorn for those useful weapons he's carrying. If you want some decent armor equipment, Steal from Thorn as well.
You'll always want someone ready to attack. When one of the twins gives the other twin a magic spell power (i.e. Zorn gives Thorn Meteor Power) you'll want to attack the powered up twin (in this example, Thorn) to eliminate their ability to use said spell. All they can do, should you prevent their spell-casting, is weak physical attacks. Pick them off after you've stolen what you wanted, and continue the story.
 
The second time you encounter the jesters is in Mt. Gulug, where they do a mock battle against Eiko. She summons Madeen and ends that battle immediately. Afterwards, the twins combine into a beast called Meltigemini.
HP: ~24,000
Drop/Reward: Tantarian Card; Vaccine
Steal: Golden Hairpin; Vaccine; Demon's Vest
This battle is pretty easy as well. Steal the Golden Hairpin and Demon's Vest if you really want them (not really necessary) and use powerful spells, summons, and physical attacks to bring it down. It inflicts Virus and Mini effects, both of which are easily cured.
Meltigemini is also vulnerable to Mini, which will both reduce its attack power and reduce its defense, making the battle much easier to complete. It's not easy to afflict Mini on it though, so expect the spell to only work after several attempts.