Personally, Duke Nukem and Isaac Clarke. Isaac is already pretty crazy, but he may be driven far far away from the edge thanks to Duke's machismo attitude. Worse, Duke Nukem is insane in his own way... :)

Something completely random and unexpected.

Link in a Legend of Zelda-modelled Tekken adventure game with Heihachi as the antagonist. He's go all Enchanted on them modern day cars.

I'd like to see Samus Aran and Master Chief in some sort of Metroid/HALO crossover.

Interesting question! However, I've noticed that I'm more prone to think of crossover between video game character and a different universe, for instance pitting Mario in a fantasy RPG. Silly example, but you get the idea.

But if I were to come up with two different characters banding together to stomp some bad guys, I'd definitely choose two similar genres akin to the combination zaymac said.

Having said that, I'd like to see Joanna Dark and Gorden Freeman tearing up an alien-infested world together. I feel like they'd be good partners that compliment each other in skill. Dark could be more roguish, able to complete the more covert type missions and Freeman would use his puzzle-solving skills to get past any obstacles. They both have experience dealing with aliens, and they both know how to use a variety of weapons. Alex comes close, but she doesn't have the experience!

That would depend entirely on the circumstances. And by that I mean the genre.
Point and click game: George Stobbart and Max (Of the Sam and Max fame)
First Person Shooter: Joanna Dark (Attractive N64 version, not slutty Xbox version) and Zoey of Left 4 Dead fame.

And of course in general the best team up would be Link and Gordon Freeman.
Just imagine the humorous custcenes.

".....*crowbar swish*"

"......HYAAAAAAH"

".....*crowbar swoosh*"

Hah, Gordon Freeman, where do your antics end...

Lara and Indy would be an obvious combination, given how much each has "borrowed" from the other over the years. I could imagine some great verbal sparring between the two and it could actually open the door for some terrific co-operative gameplay!

Mario and Sonic. Smash Brawl was a nice teaser but I'm hoping that one day those two'll team up in an actual game.

Sam Fisher and Solid Snake. Terror cells wouldn't stand a chance!

Guybrush Threepwood in a Metal Slug game.

:3

Delta from Bioshock 2 and the Overlord from Overlord!

@ itsjustaar: You fight like a dairy farmer!

Jill from DrillDozer and a Big Daddy.

Morrigan from Dragon Age and Nick from Left 4 Dead 2. Zombies, Darkspawn, whatever. I just want them to be drier than a martini in a sandstorm.

Chell and Freeman. It's gonna happen. It's gotta happen.
I'm hopeful. =D

First and foremost, Mario and Sonic in a sort of co-operative adventure style game. None of this Olympics crap. Sounds very fan-boyish, but I think it could potentially be a great game.

Also, I think maybe a beat-em-up with the characters from Mortal Kombat and Street Fighter would actually be pretty awesome. Something that's as good as (but obviously a lot better) Streets of Rage 2. Possibly with some platforming elements, RPG elements, that sort of thing. If done right, I think it'd be really rad. Subzero and Ryu forming a tag team, Scorpion and Akuma. I'd say it'd be rad.