I love the Batman and joker rivalry of course but black Adam and Shazam is really good to.
Batman & Bane, Flash & Eobard Thawne. I really love the relationship between Flash and the Rogues as well.
Wally West Flash and Abra Kadabra.
Captain Picard- Q
Optimus Prime - Megatron
Batman - The Penguin
Captain Janeway -Borg Queen
Superman - Metallo
Spider-man- Green Goblin
Stargirl - Shiv
The Incredible Hulk - The Leader
I always liked the rivalry between The Shade and the Ludlow family.
Green Lantern and Obsidian.
Superman - Darkseid
Starfire - Blackfire
x-men - Apocalypse
Spider-man - Carnage
Ninja turtles - Shredder
Batman - Ra’s Al Ghul
Swamp Thing - Arcane / Rot
Green Arrow - Merlyn
Favorite all-time hero/villain rivalry has to be Spider-Man and The Green Goblin.
Batman- Joker
Superman- Luthor
Wonder Woman- Cheetah
Capt. Marvel- Black Adam
Nightwing- Blockbuster
Power Girl- Ultra-Humanite
Zatanna- Alura
For rivals, I would say
Green Lantern (Hal) and Sinestro
Aquaman and Ocean Master
In many ways each wants the same thing, but use very different tactics.
Martian Manhunter / Kanto