In terms of star power and charisma, Sean Connery(James Bond) and Harrison Ford(Indiana Jones) were the most high profile pairing in a movie

There will never be a pair like Redford and Newman. I think they will always be the classic movie duo that all others will try to emulate in some way, but will fall short. This movie is genius. Yes, it has a great script and great directionbut the reason it's forever one of the best movies of all time is because of the undeniable, unforgettable, chemistry between Redford and Newman.

Arnold and Sly!
4 8 15 16 23 42

For me Redford and Newman were the best.
I know all to well that movie history has an abundance of great pairings of actors and actresses but these two are my all time favorite.
After The Sting came out I waited 35 years for them to make another movie together but it never happened, I heard them say for years if they ever found the right script they would love to work together again.
I guess it just wasn't meant to be.
I am happy we got the two movies we have.

Slow to the party, but I was inspired.
While there never has been, nor ever will be a pairing like Redford and Newman, I will suggest the following:
Redford and Morgan Freeman in An Unfinished Life ( I loved Redford as the cranky old man character, he did it perfectly)
Susan Sarandon and Geena Davis in Thelma and Louise (no one said it had to be all about male actors and movie buddies)
Kathy Bates and Alfe Woodard in The Family That Preys (excellent on screen together)
Susan Sarandon and Goldie Hawn in The Bangor Sisters
I'm sure I'll think of five more after I post this.
BTW: the other Redford/Newman film The Sting was wonderful, but I seem to fixate on the taps on Redford's shoes while he is running through the streets so many times in that movie! I can hear them now. He must have been getting lots of exercise with all that running. I wonder if the taps ever made him slip on those paved streets? Did he speak as many minutes of dialogue as he spent running around? All in fun, I love the movie, but those taps
I may be a little prejudiced about the never will be comment, but hey, Redford has been the lust of my life since Sundance.

Hope and Crosby in the road pictures.
"Fasten your seatbelts. It's going to be a bumpy night"

I agree with some of the previous posts. Caine-Connery pairing in the Man Who Would Be King is great. Mel Gibson-Danny Glover is good. Let me throw some more. Jack Lemmon-Walter Matthau in several movies. Likewise Woody Allen-Diane Keaton. William Shatner-Leonard Nimoy in Star Trek. Simon Pegg-Nick Frost in Shaun of the Dead. Tom Hanks-Tim Allen in Toy Story. Not a duo but Roy Scheider, Robert Shaw and Richard Dreyfuss were a compelling trio in Jaws.

I haven't read this whole thread, and some great movies, and pairings have been mentioned
But most the movies I saw mentioned were one time events for the pair
I cannot think of a pairing as successful as Redford and Newman in multiple movies, and where they became great personal friends
There's the Mel Gibson, Danny Glover franchise, same movie really 3-4 times, and I get the feeling they didn't like each other off set, or didn't gain the friendship that Newman and Redford had
You don't have to stand tall, but you have to stand up!

Burt Lancaster
and
Kirk Douglas
were in seven movies together.
Pretty high-wattage in talent, looks, and star power!

Love this pairing, I think it elevates the movie beyond compare.

Best pairing history.

Harrison Ford and Shortround!

I honestly can't think of a pairing with the chemistry that Newman and Redford have.
"I'm too old for this $hit"-Roger Murtaugh (Lethal Weapon)

I really liked Bridges and Goodman on The Big Lebowski

I like these pairs too
Clint Eastwood and Eli Wallach in "The Good The Bad and The Ugly"
Paul Newman and Robert Redford in "The Sting"

Danny & Rusty (Clooney & Pitt)
Vincent & Jules (Travolta & Jackson)

Don't get me wrong, Stakeout is a fun movie, though I'll never see Another Stakeout because it's just the same plot as the first, just with the addition of Rosie O'Donnel, who is utterly disgusting. But Dreyfuss and Estevez is your idea of an "epic" pairing of actors? Dreyfuss is a decent actor, but Estevez would never have been famous, even as brief as his movie career was, if not for being Martin Sheen's son. Just seems like an odd choice. De Niro and Pacino, Eastwood and Hackman, De Niro and Pesci, are examples of amazing actors being paired together. Estevez and Dreyfuss doesn't even come close to the previously mentioned pairings. Now if you had said Dreyfuss and Bill Murray from What About Bob?, then you'd be more on the right track.
Just like the tide out at sea, we lower & rise again

I like your choices! And if we're talking westerns, J. Robbards and Charlie Bronson in Once Upon a Time in The West

Kurt Russel and Val Kilmer in Tombstone
Tommy Lee Jones and Robert Duvall in Lonesome Dove

Dustin Hoffman and Tom Cruise in RainMan

Emilio Estevez and Richard Dreyfuss in Stakeout, and Another Stakeout. Those are also two great films with great chemistry between the two actors!

Even "The Color Of Money"?

I consider Robert DeNiro to be the most overacted actor ever, and not only does Raging Bull suck but so dodare I say itall of Scorcese's films, even Good Fellas is barely watchable.

I would place Robert De Niro and Joe Pesci in Raging Bull slightly higher. It's pretty hard to beat that pair. If you're referring more to how attractive the two men are to women than how well they look together on-screen, then yeah, Redford and Newman would probably gain the top spot.