Dr. Doom vs. Ra’s al Ghul. Two willful would-be world conquistadors, just one world to be conquered. Let the machinations begin!
Rick Jones vs. Snapper Carr. 
(And yes, I know about the unofficial “crossovers” those two have had)
Bracketing mine.
While I admit the odds don’t look good, I suspect Nightwing could more than hold his own against Spider-Man.
Any of classic Teen Titans from the Wolfman/Perez era could hold their own/ beat Spider-Man: I’m particularly jazzed by a Spider-Man/Wonder Girl and Spider-Man/Cyborg match-up.
When and where did Batman vs. Captain America take place?
That’s happened at least twice. Once, there was a crossover that took place in WW2 (was that the Byrne one E-Sabbath?) and also during the big DC vs Marvel crossover.
I’m going to give that one to Batman. Roland’s gun-handling is his big ju-ju. Batman has defeated hella gunmen before, notably Deadshot.
On the comedy side…
The Tick Vs. Spider-Man
The Tick Vs. Bizzaro
American Maid Vs. Wonder Woman
Fishboy, Crown Prince of Atlantis Vs. Aquaman
Barry (the other Tick) Vs. Captain America
The Human Ton and Handy Vs. Juggernaut
The Terror Vs. Magneto
Thrakkorzog Vs Martian Manhunter
What, exactly, are Batman’s strengths? Besides the gadgets, all he has is brains, resourcefulness, ethics, iron will and a steely sort of charisma. Roland can match him in all of those. Gun-play is the least of his ju-ju.
To pute it another way - Roland is always prepared.
Dr. Strange vs John Constantine
Which would mainly be the type of confrontation where Strange enters his Sanctum one day, and sees John sitting there smoking a silk cut, grinning, with a line drawn in front of him made of bone chalk, and the portal to Hell yawning behind him.
Superman vs the Hulk
and not that lame encounter where Superman anchored himself to the ground so all of Hulk’s punches conducted through and dissipated through the Earth’s layers. I want buildings flying everywhere, gigantic canyons collapsing, mountains being tossed around, the whole nine yards.
Three times…
In JLA vs Avengers they fought to a draw countering each others’ moves until Batman concedes that given time Cap could beat him. Much better than Cap getting clunked by a batarang after being knocked off his feet by a wave in the sewers.
I think you might be thinking of Deathstroke, The Terminator. Nemesis to the New Teen Titans for a long time, I believe. (Yes, the movie people had to pay DC for the use of the name.)
It’s kinda weird that I know that. Never read Teen Titans, but had a good friend who was ga-ga over them in the early '80s.
Just for starters, there’s Batman’s enormous genitals. I read the Gunslinger books up through Wolves of the Calla, and I frankly don’t see Roland’s skillset being all that useful in going toe-to-toe with The Bat. For what Roland and his associates had to accomplish, his knowledge of The Beam and related topics was invaluable, no doubt about it. However, when it comes down to combat, Roland is just one more guy who is really, really good with a gun. Batsy made lots of gunmen his bitches over the years.
Actually, you left out the deciding factor: hand to hand combat. Roland may be a bit faster on the gun than Batman is used to, and more accurate to boot, but he’s still just a guy relying on his gun. If (I think when, but I’m trying to be fair to both sides) Batman disarms him, the battle is over fast.
Askia, or I suppose anyone. How would Nightwing be able to give Spider Man a run? He’s a top athlete, but Spidey is well beyond that with the added bonuses of webbing and a top notch danger sense. I’m not seeing how Nightwing is even going to lay a glove on the webbed wonder.
P.S.: Hey absent Askia. How’s that Swap story coming? 
I’m claiming the time-honored “home turf” tactic and some inspired cheating in my scenario – but – assuming they fight in Bludhaven, and Nightwing has a stash of police-issue riot gear for his personal use within grabbing distance from his day job as a cop, I can see him giving Spidey conniption fits with mace, pepper stray and tear gas.
I can see a very Merry Christmas gift for fans of that storyline. 
Well, if you’re going to go the merciless slaughter route:
Berserker Wolverine vs. Aunt May [Homer]I hate her so much[/h]
Yeah, inspired cheating goes both ways. I’m throwing in the unipowered spider man. How do you like them apples?
Christmas nothin’. My birthday is tommorow and I at least expect one heck of an explanation.
-Harassing Harborwolf
Batman vs. Doctor Manhattan.
A more human battle…
The Punisher vs Green Arrow.
Both men great with weapons. But with all the human foibles.
Let the battle begin.
Kind of a different one:
In a faraway place, two continents away, there is a vast desert, barren of water, shade, and hope. Nestled deep in the center of the desert stands a tall mountain range, jagged and airless, frozen forever in its web of glaciers. Tucked high in the mountains is a jungle dark and solemn, its gloom punctuated by the cries of strange animals and the mutterings of men lost to the world. In the middle of the jungle lies a deep still lake, with a single island watched over by a fallen temple. And buried deep in the heart of the temple is the fabulous Lion’s Heart, a ruby the size of your head.
At one end of the desert, Tintin, intrepid boy reporter for the Petite Deuxieme, grasps his staff and calls Snowy. At the other, Scrooge McDuck, richest duck in the world, completes his mental money count and summons Huey, Dewey, and Louie from their Junior Woodchuck manuals. One will triumph over the obstacles and carry home the prize. The other will have a run-in with an over-lucky gander and spend the next six months teaching the natives about Belgium. The race is on.
That, and I want to see Wolverine kick Batman’s ass, just for fun.
I’m sorry, but ain’t now way no how freaking Nightwing could come close to dealing with Spider-man. Spidey has pretty remarkable super strength (on par with some heroes where that’s their only schtick), reflexes that are insanely wuperpowered, and a spider sense to know when someone is up to a trick. Freaking Batman couldn’t take on Spidey, unless you assume that he could research out a way to find one of the chemicals some villain of Spidey’s or another used to take out his spider-sense.
I don’t think any of the classic Teen Titans would have a chance in the world, and it’s likely Spidey would have an OK chance of taking the whole team on at once, as he has extensive experience fighting whole groups of second stringers.
Nightwing?? For crying out loud, you yourself personally would have a better chance taking out a tank with just your bare hands.