Well, Zangoose and Seviper obviously.
Durant and Heatmor are obviously meant to be enemies.
Same goes for Shelmet and Karrablast.
Meowth and Murkrow steal from each other.
The two forms of Basculin are said to be enemies.
And several legendaries: Groudon & Kyogre, Cresselia & Darkrai, Reshiram & Zekrom.
(As I recall, Dialga and Palkia were only enemies in the anime.)
Those are the only confirmed ones I can think of at the moment.
And then there's some that are speculation. Lucario and Zoroark for example. To begin with, there's the fact that Fighting and Dark are conceptual opposites. (Fighting with honor vs using dirty tricks to win.) Plus they played a very similar role in their generations. They were both "Mascot Pokemon"; among the first revealed for that generation, used to promote that generation pre-release, non-legendaries who got their own movies, and both come from two-stage lines. But what's most interesting is that they have opposite powers: Zoroark creates illusions to deceive people, while Lucario has the power to see the truth. Zoroark creates illusions and Lucario sees through them.
Pinsir and Heracross might be one, due to the this common Japanese trope. Heracross is part Fighting-type and Pinsir learns many Fighting-type moves by level up.
I've always felt that Camerupt and Waillord were related. Not enemies, but just counterparts. They're both 2-stage lines from 3rd Gen and their types personify Team Aqua and Team Magma.
There's a lot of other Pokemon that are counterparts, but not enemies, too many to list. Arcanine and Ninetales, Solrock and Lunatone, etc.