Ras Al Ghul vs. Green Arrow 
Darkseid vs. Doom Patrol or the JLI 
Bullseye vs. Black Widow 
Iron Man vs. The High Evolutionary  
Black Panther vs. Loki 

Carnage vs Wolverine

I always found it odd that Red Skull never tried to take out the x-men at least once. 
dr doom vs the defenders 

Daredevil fought Doc Ock at least once back in the 80s... And won. Songbird doesn't actually produce sound anymore, as far as I know. She makes hard-sound constructs IIRC. People have tried to overload his senses in the past. Most of his rogues have tried that at one point or another. And Daredevil's biggest weakness is Matt Murdock, which is something that Kingpin has demonstrated a lot in the past.

2:32 --- Norm Chan, very proud of his sonar-resistant arms idea.

Shocker vs. Daredevil

thing is a lot of these villians are kinda tailored to the particular hero.  Sure there can be some cross-over but regardless..they're kinda tailor made.
 
Though it was always interesting to see Doom and Iron Man go at it.

black panther vs. prometheus 
war machine vs. cyborg superman 
luke cage vs  clayface   
young justice vs. suicide squad 
 iron fist vs. deathstroke 
iron man vs. brainiac 
silver surfer  vs. superboy prime 
 blade vs. etrigan 
the avengers  vs. injustice gang 
wolverine vs.  jason todd 

Juggy vs. Power Pack is an awesome idea
U-Foes vs. FF
Black Tom Cassidy vs. Moon Knight

Red Skull vs The Hulk, yeah I'd love to see Banner hold back old green genes while he tries to stay a step ahead of the Red Skull. That would be very kewl. 

Mr. Sinister Vs Spiderman - as long as it doesn't end up as another clone saga!

I would REALLY like to see Batman get some of Superman's villains. Obviously not Doomsday since it would be too much but enemies like Luthor and Parasite would be cool.  
The difference in Bat's and Supes' power levels is just so great that I would love to see the change in the approach to fighting the villains.

Daredevil vs. a sonic villain sounds awesome and not ninjas dude!!! The Rogues Vs. Batman stuff sounds awesome too but I think the Rogues kinda look like some of Batman's villians so I think he can beat them.

I'd like to see uber-powerful villains take out the less powerful heroes to thin out the ranks, and then go after the upper tiers.

Rampage vs She-Hulk and Rogue vs Wonder Woman would be interesting.  
 
Villianwise, Lex Luthor vs any of the classic JLA aside from Supes would be interesting.  
 
How about Masters of Evil vs Fantastic Four or Brotherhood of Mutants vs the Avengers? 
 
Thor vs Abomination?  
 
Superman vs Black Adam?   
 
Always wanted to see Lex Luthor vs Doctor Doom...
 
Hmm...

Personally I think some of Batman's villains should team up.
Penguin with all of his money will recruit The Riddler, Killer Croc, Clayface, Mr. Freeze, and The Mad Hatter. And with Penguin leading the group they'd create "The Black Owl Organization." One reason for them doing this because some gang is taking over Gotham and making them look crappy. So they join together to take them on, and other teams like The Secret Six(Croc vs Bane?), or the Teen Titans. Also Penguin could upgrade his umbrella along with other equipment to make a very villainous team.

1 I'd like to see some villain vs villain sometime no heroes at all.
 
2 And it won't happen but having batman take on some of spider-man's enemies would be an upgrade and challenge for him.
 
3 And Captain America take on Gotham's worst. 
 
4 Dr. Doom take down Ironman
5 Maybe Xmen trapped in Asgaurd for a while with Thor gone and they have to hold the fort against the wave of monsters, trolls, frost giants etc. 
 
6 Blade fight the Hand
7 Punisher take on Vampires. 
 
8 Thor take on some of Dr. Strange's demon enemies.   (this story could blend with number 5)
9 Yellow Lanterns attack Superman
10 Luther targets a green lantern

I always hate the cop outs that writers will use like some type of interruption between the fights that causes them to band together or that they just give up on each other because there is a new threat. 

I'd love to see Darkseid crash the MARVEL earth rather then the DC earth, see if all the marvel heros can even come close to pushing him back