Well, seeing as Fenris ain’t here to give us a comprehensive list of obscure heroes and their arch-nemesis, I’ll toss out a few to keep the Teeming Millions satisfied.
Atari Force: The Dark Destroyer
Amethyst, Princess of Gemworld: Dark Opal
Maggie Simpson:That Baby With One Eyebrow.
I suppose the criteria for determining an arch-nemesis is
multiple engagements:
Captain James T. Kirk vs Kahn Noonian Singh
Captain Jean-luc Picard vs Q
Captain Benjamin Sisko vs Gul Ducat
Captain Kathryn Janeway vs Borg Queen
Dr. Who vs The Master
Elvis Presley vs The Beatles
Evel Kinevel vs gravity
Commander Adama vs Lord Baltar
Optimus Prime vs Megatro
Howard Stern vs the FCC
Iron Man = The Mandarin
Groo = cheese dip
Buffy::Angelus
Angel::Angelus
Robert Mapplethorpe::Cincinnati
Flash: Reverse-Flash
Legion of Super-Heroes: Time Trapper. I’m very tempted by the thought of the Fatal Five or Mordru, but somehow the “time travel” element seems so essential to the Legion’s history that it makes the Time Trapper seem like the villain who most challenges the essence of the team.
Adam Warlock: Thanos
Hank Pym: Ultron
He-Man: Skeletor
Green Lantern Alan Scott: Solomon Grundy
Sherlock Holmes/Professor Moriarty
Nero Wolfe/Arnold Zeck
Robin Hood/Sheriff of Nottingham
Dick Tracy/Pruneface
Harry Potter/Voldemort
James Bond/Blofeld
Encyclopedia Brown/Bugs Meany
Steve McGarrett/Wo Fat
Flash Gordon/Ming the Merciless
The Maxx/Mr. Gone
Generation X/Emplate
Duncan MacLeod/Kalas? (Horton? Xavier?)
Connor MacLeod/Depends which movie(s) you believe in. Kell makes the most convincing case…
Austin Powers/Dr. Evil
Luke/Vader
Han/Jabba
Frodo/Sauron
Londo Molari/G’kar (Which one’s the hero, though?) 
GI Joe/Cobra Commander
He-man/Skeletor
The Powerpuff Girls/Mojo Jojo
Nick Knight/LaCroix
Ripley/The aliens
(BTW, the best example on this whole thread, I think is Sisko/Dukat. What a great relationship! 7 years of hatred, mistrust, and kinship…)
Doc Savage: John Sunlight
The Fabulous Furry Freak Brothers: Norbert the Narc
The Avengers (Marvel Comics): Kang the Conqueror
The Sub-Mariner: Destiny
The old X-Men: Magneto
Cerebus the Aardvark: himself
Buck Rogers/Killer Kane
Nayland Smith/Dr. Fu Manchu
Dr. Jeckyl/Mr. Hyde
Rog Blake/Servilan
James West/Dr. Miguelito Loveless (Michael Dunn only!!!)
Human Torch/Sub-Mariner
James Bond/Ernst Stavro Blofeld
U.N.C.L.E./Thrush
Control/Kaos
Terry Lee/The Dragon Lady
No, no, no…Spider-Man’s nemesis has always been Peter Parker. Not in the traditional villain role, but in the sense that his life is always a struggle between the webs and the man beneath them. Does he visit his sick aunt in the hospital or stop Dr. Octopus? Go on a date or stop the Green Goblin? This is why Peter is notorious for tossing his costume in a trash can…and, of course, why he always puts the costume back on.
Lester Girls::Lily Lee, the Lizard Lady
Also General Poon Tang and (the slippery) Ben Wa.
Adam Warlock VS The Magus
Warlock and Thanos have been allies numerous times. Warlock’s old nemesis was ManBeast. ManBeast is one of the few nemeses to stay beaten. Warlock’s then gained a new nemesis in the Magus. Magus keeps returning, and Warlock has to team up with Thanos to beat him. If you have to consistently team up with a villian to beat a second villain, villain #2 is your Nemesis.
The Heckler Vs Boss Glitter
The Heckler fought Bushwack’r once IIRC. He also fought El Gusano, Cabbage Head, only once. But, the same evil mastermind controlled those villains: Boss Glitter. They never actually met, but the writers were clearly setting Glitter up as the nemesis.
The Heckler Vs Low Sales
That is what ended the comic. The Heckler plunges a thousand feet or so and lands in a pile of trash
Heckler-Don’t worry kids! It’ll take more than that to kill the Heckler!
Editor-Yeah, it’d take lousy sales figures.
Heckler-Yeah, that’d do it.
Flaming Carrot Vs Don Whiskerando
Captain Ultra Vs A Bic Lighter
I’m amazed at how many heroes have permanent, evil doubles-Hulk/Maestro, Flash/Reverse Flash, Warlock/Magus, SpiderMan/Venom etc. The Maestro IMHO should have stayed dead. The Green Goblin should have remained Spidey’s arch foe.
The Teenage Mutant Ninja Turtles- Shredder
The World War I Flying Ace- The Red Baron
Homer Simpson- Mr. Burns (in the rare instances he can remember who Homer is)
Cecil Adams vs Marilyn Vos Savant
Groo doesn’t have an arch-nemesis on the grounds that none of them live long enough to become one.
John Crichton / Scorpius
Worf / Duras and his sisters, L’ursa and B’etorr
Zorro / Captain Esteban
Particle Man = Triangle Man (They Might Be Giants) 
Zev Steinhardt
Wasn’t Captain Ultra cured of his pyrophobia back in Marvel Comics Presents #50?
I am such a geek…