Batman vs Lex Luthor is a good one. Basically the two wealthiest, most intelligent and manipulative skill-monkeys in DC would make great opponents in a chess master sort of way.
Dr. Doom and Iron Man have had a few confrontations over the years, but you'd think they'd do so even more regularly. Tony is a man who was born into wealth and power, but learned humility when his life was saved and has since tried to use his wealth to better the world (when the writers weren't making him Iron Hitler). Doom was a man born into poverty who mastered science and sorcery to take over his country and has dedicated himself to taking over the world. Tony is basically the modern capitalist trying to improve the world, Doom is old school monarchy trying to build an empire.
Iron Fist versus the Mandarin seemed like something that could have happened as well. The Mandarin vs Iron Man was always good for the whole "ancient Eastern mysticism and martial arts" vs "modern capitalist science and technology", but you could see the Mandarin having just as much of a problem with Danny. Danny is another billionaire with a corporation, but he's also someone steeped in eastern mythology, which the Mandarin might hate as seeing some white infidel bastardizing his people's traditions. Could make for a cool fight and take a jab at the Mandarin's own racism. Though it might be weird that the Mandarin's big opponents both have 'Iron' in their name.
Given that the Rock of Eternity sits in the heart of existence and allows those bonded to it (Shazam, the Marvel Family, Black Adam) to travel through time, space and dimension, you wonder why more comics don't have Cap, Mary and Freddy policing the timeline and keeping extradimensional invaders out of the DC Universe. Stuff like Booster Gold's series would work great for them, and fighting invading mystical beings in the Cthulhu/Trigon vein would be right up their alley.
Has Kraven the Hunter ever fought Wolverine? You'd think a showdown between the two most 'hunter' focused archetypes would be a given.
There's a lot of street level types that you feel like Arcade should have fought more of, before stuff like Avengers Arena and that Avengers Academy crossover basically ruined the guy. Him being hired to kill Capt. America, Iron Fist & Luke Cage and the like could have made for some fun adventures. Throw Danny and Luke into some 70's style Kung Fu/Blacksploitation scenarios for a little extra adventure. The Heroes for Hire thing works as well since Arcade, Danny and Luke all are mercenaries to some extent.