Computer: Phineas! versus, Phineas!

Phineas: Well, at least I'm evenly matched.

Leela: We're exactly the same, I know all her moves. Therefore, I have the upper hand. Hiiyyyya-ow!
(Leela and her Alternate Universe counterpart do the exact same kick and knock each other unconscious)
Professor Farnsworth: Now, now; perfectly symmetrical violence never solved anything.

McGee: All right. Ooh, okay - Gibbs versus...

(Gibbs walks up behind Abby)

McGee: Gibbs.

Abby: Oh, oh that's good! Okay, so um, evil twin or a clone?

Kefka Palazzo: Who's that handsome devil?

Jecht: I get to fight with the best fighter in the world!

Cloud: Not you again.

"Aw, man, SHADOW Homestar? 'Hey, I've got a wonderful idea! Let's dip the main character in a vat of ink and make you fight him before you get to the end boss!'"

Snake: Colonel, it's me! I'm fighting myself!
Colonel: Snake, what's going on out there?! Could it be...? Has the "Les Enfants Terribles" project really come this far?!
Snake: It's more than that! He's got my moves, my gear... It's like looking in a mirror!
Colonel: Do you think they collected data on you, and created another Snake?
Snake: He's got the same build, too. Creepy. But his Sneaking Suit is a different color. And his tactics are slightly different.
Colonel: Interesting. So even if you're evenly matched in power, your fighting styles will make a big difference. You've faced tougher odds in the past, Snake. Don't let this impostor beat you!

Just what I need, another clone.

You know, I remember reading somewhere that there are only two truly meaningful things you can do with your doppelganger when you're locked in a room. You can fight them... Or f#@k them.

If I can defeat myself I will become complete!

Twilight: They're changelings, remember?

Fake Twilights: They're changelings, remember? (evil smile)

Yellow Lantern: Sanctimony is easy when you know what-

Green Lantern: Save it. Time to kick my ass.

(one fight later)

Green Lantern: Well, that was surreal.

Wonder Woman: And a bit disturbing.

Green Arrow: Yeah, all of that yellow is really tough on the eyes.

Insurgency Batman: You're good.

Main Universe Batman: You expected otherwise?

or

Insurgency Batman: Call it a draw?

Main Universe Batman: Not our style.

Regime Superman: I tried to save this world!

Main Universe Superman: Now I'll save it from you.