What are some famous arch-rivals?

There are many classic nemesis characters in modern fiction. But I was wondering about classic arch rivals - the kind of character who matches the genius of the antagonist and tries to outdo him at every given opportunity. The antagonist and the arch rival are typically bitter enemies, but secretely respect one another as professionals and sources of inspiration.

Holmes vs. Moriarty springs to mind.

Hm. Seaton and DuQuesne might fit. But they’re not exactly modern.

Reggie Mantle, surely.

Wouldn’t Moriarty rather be a nemesis? I don’t recall Moriarty’s background, but I think of him to be a murderer of some sort.

He wrote both A Treatise on the Binomial Theorem at the age of 21 and later The Dynamics of an Asteroid, so he was a pretty smart cookie.

Tom and Jerry.

Wile E. Coyote and the Road Runner.

And lest you disagree, I think there was lots of respect amongst these antagonists.

Why yes, my tastes are quite highbrow…why do you ask?

I think I know what you’re getting at: the rivals are both going after the same goal, but each is trying to get there first. It’s more like Holmes vs. Lestrade (though that’s not a perfect example) than like Holmes vs. Moriarty. Unfortunately, I’m not coming up with any really good examples right now.

Holmes was Moriarty’s nemesis, not the other way around.

First to mind, Superman vs. Lex Luthor, then Batman vs. Joker. I guess every superhero has a main villain.

The OP seems to be more about two antagonists trying to out do each other, not do each other in. Not classical, but Professor Farnsworth and Professor Wernstrom on Futurama fit the bill.

Donkey Kong/Bowser and Mario. L and Kira from Death Note, although perhaps in this latter case they are more like nemeses.

Piccolo and Goku from Dragon Ball Z.
Dexter and …what’s-his-name, from Dexter’s Lab

Gah! There are tons but I’m having trouble thinking of any. Villians or nemeses are much easier to find.

Edison v. Tesla?

Mandark.

I think the OP means something more like Dr. X versus Magneto.

The Brain and Snowball

The Great Leslie and Professor Fate.

Darkwing Duck vs. NegaDuck.

Man, that was a serious feud.

Indiana Jones and Belloq.

Sherlock Holmes and his brother, Mycroft

Cain and his brother, Abel

Romulus and his brothr, Remus

The two gunfighting brothers in the movie Cat Ballou

Annie Oakley and her later-to-be husband, Frank Butler (“Anything you can do, I can do better…”)

Reed Richards and Dr Doom