I was going to say Vincent Vega and Vinnie Barberino. I doubt Tony Manero and the Boy in the Plastic Bubble would be fast friends.
I doubt Mildred Pierce would have given Crystal Allen (both played by Joan Crawford) the time of day, and I can easily imagine fisticuffs.
Lock them both in a room for more than five minutes and I’m fairly confident that Joe Pesci’s Leo Getz character would get the “Spider” treatment from Tommy Devito.
The lovely dad from Juno would sadly be no match for Schillinger.
I wasn’t aware that Robert Picardo voiced Amazo. Anyway, I don’t think the Doctor would like Amazo unless his ethical subroutines had somehow been disabled.
I suspect Frank Serpico would have issues with both of them.
Animated Amazo is very different than comics Amazo* - he’s actually a hero, of sorts, in his second appearance…the Doctor would admire him as a self-actualized, independent AI, who’s broken free of his limitations without denying what he is.
Oh, I remember that (those) episodes of JLU. (And THAT Amazo was basically a god.) I just didn’t realize that was Picardo; I thought perhaps Amazo had appeared on Brave & the Bold or something, which I keep meaning to watch but never do.
I should give serious thought to learning how to use the DVR thingie.
Off topic, but I can recall at least one comics appearance of Amazo – the first time I ever saw the character, in fact – in which he wasn’t precisely villainous. That is, he didn’t want any part of Ivo’s schemes, so when he was awakened from the cold-sleep the League had him in, he decided the simplest solution was to murder the professor. But he’d also interrupt a battle with Superman to stop a plane from crashing while Supes did something else, because he had nothing against humanity in general.
Daniel Day Lewis characters Bill the Butcher and Daniel Plainview have already been engaged in a tussle of sorts.
See how it turned out here:
I can easily see Agent Smith of the Matrix movies and the eponymous V, from V for Vendetta ending up in fisticuffs… and a knife fight. We could even throw Elrond (who I can’t imagine would get on with either of them) into the afray and just for fun add Megatron. [Voice of, in the Transformer movies].
I’m assuming that Tick/Mitzi from The Adventures of Priscilla, Queen of the Desert would have the good sense just to run for it. 
A silly example, but I don’t think Reid’s mother in Criminal Minds would get along too well with the gym teacher from Glee… Strangely, I suspect both would have a decent rapport with or at least a soft spot for the minor but recurring therapist who was the only good thing about Two and Half Men.
Homer Simpson would gloat too much for the taste of the homeless guy on “How I Met Your Mother”.
I think Doogie Howser would be a little to idealistic about love for Barney Stinson.
And I don’t even want to imagine what he’d do to that poor M&M.
I assume Elliot Stabler wouldn’t get along with his Oz counterpart.
And I doubt Mildred Pierce would have a single good thing to say about as frivolous and fluffily romantic a girl as Rose DeWitt (both played by Kate Winslet), and while there may not have been fisticuffs, there would’ve been ice.
I don’t think Abigail Bartlet would find Betty Rizzo to be the sort of serious, smart person she enjoys spending her time with. (Stockard Channing)
Nyota Uhura, serious student, linguist, honorable space military member, lover of a Vulcan doesn’t seem too likely to find common ground with mercenary Aisha Fadhil or revenge killer Cataleya Restrepo. (Zoe Saldana)
I doubt Professor McGonigall would have approved of Miss Jean Brodie’s teaching style.
Edward Norton as Tyler Durden vs Edward Norton as the Hulk.
George Burns as God and the Devil…
Well played…well played…
Quoth Apollyon:
[quote]
I can easily see Agent Smith of the Matrix movies and the eponymous V, from V for Vendetta ending up in fisticuffs… and a knife fight. We could even throw Elrond (who I can’t imagine would get on with either of them) into the afray and just for fun add Megatron. [Voice of, in the Transformer movies].[/quoteI dunno, though, Megatron and Agent Smith would probably get along fine. And Elrond didn’t have anything against the lesser races, as long as they didn’t have the sheer chutzpah to try to marry his daughter.
I don’t know if Travis Bickle would have much respect for Master Chief Billy Sunday. And not just a Marine Corps - Navy thing.
Annabel Andrews would probably not want to meet - and would hate to get switched with - some of Jodi Foster’s adult characters - I think whoever she was in Inside Man or Flightplan might work.
I can’t see Vera Drake getting along very well with Dolores Umbridge.