In Shakespeare in Love, Geoffrey Rush repeatedly utters the phrase “It’s a mystery.” Last week I saw Shine for the first time, and he repeatedly uses the same phrase in that as well. It was obviously no coincidence.
Any other movies where this happens?
Marlon Brando in The Freshman is an obvious one.
Ahh-nold’s repeated “I’ll be back” is another. Other than that, all I can remember offhand is William Daniels, in an episode of “St. Elsewhere” in which he and his wife visit Philadelphia, singing the city’s name as sung in “Piddle, Twiddle and Resolve” from 1776.
Robert DeNiro’s “Are you talking to me?” from The Adventures of Rocky and Bullwinkle.
Seriously.
John Cleese’s character “accidentally” addresses Jamie Lee Curtis’s character as “Wanda” in the movie Fierce Creatures, in reference to the earlier film A Fish Called Wanda, also starring Cleese and Curtis.
Not movies, but one I found amusing was Ian Richardson, as Death in the recent Hogfather TV adaption, saying “YOU MAY THINK THAT BUT I COULDN’T POSSIBLY COMMENT…” 
John Lithgow repeating his rock and roll speech from Footloose in an episode of 3rd Rock From The Sun.
It’s not really the same quote, since someone else says it, but Barbara Streisand saying “Love means never having to say you’re sorry” to Ryan O’Neal 9who said it in Love Story at the end of What’s Up Doc
Other near-misses (not the actor quoting a line from another film) are Sean Connery as James Bond saying to the nurse “Another Time, Aother Place” (The name of a movie he’d just been in) in Thunderball, and Sean Bean as Boromir in the Fellowship of the Ring feeling the shards of Anduril and saying “Still sharp”, after playing Richard Sharpe.
Danny Glover has said “I’m getting too old for this sh*t.” in a few places since Lethal Weapon.
I can’t remember any right now, though.
Danny Glover has a cameo in Maverick, where he utters his staple “I’m getting too old for this shit” line from the Lethal Weapon movies. Mel Gibson of course plays Maverick.
“You have no idea.”
Jeremy Irons in Reversal of Fortune.
Jeremy Irons, as the voice of Scar, in The Lion King.
Kevin McCarthy shouting “You’re Next”, “They’re Coming”, and the like in the 1956 and the 1979 versions of Invasion of the Body Snatchers. (He’s shown carrying a pod, but I’m not sure if he says it again in Looney Tunes: Back in Action in 2003)
My favorite (though not quite the OP):
In 12 Monkeys, Bruce Willis says “Everyone I see is dead.” Which is pretty close to “I see dead people” from a later Willis film.
Not dialog, but George Raft often would be shown flipping a coin, a reference to his role in the original Scarface.
In His Girl Friday, Cary Grant refers to someone as “Mock Turtle” – the part he played in the Paramount Alice in Wonderland. He also uses the name “Archie Leach” – his own real name.
“Say, would you like a chocolate covered pretzel?”
Of course, Jason Lee is Brodie Bruce in both Mallrats and Jay and Silent Bob Strike Back. In Mallrats, he says the line in context. In Jay and Silent Bob Strike Back, he’s clearly just referencing Mallrats.
Sure, except that a) That’s not a tribute to the earlier role, and b) He never said the 2nd line. Haley Joel Osment did.
Not a direct quote, but in the movie Evolution, Orlando Jones asks, “Shouldn’t we call the government to help us out on this?” David Duchovney responds, “Absolutely not! I know those people.” Clearly a reference to his paranoid, Fox Mulder character on the X-Files.
Kirk inverts Spock’s Vulcan axiom “The needs of the many outweigh the needs of the few, or the one” from *STII: The Wrath of Khan * after helping bring him back to life in the next movie, STIII: The Search for Spock.
Teri Hatcher had a cameo ( I think) in a Bond movie (Tomorrow Never Dies? Maybe?) during her tenure as Lois on Lois & Clark. I forget her exact words, but she said something to Bond which was very reminiscent of the type of things she said to Clark, about his more or less unexplained absence.
Variant: My Little Chickadee ends with Mae West and W.C. Fields quoting* each other’s famous lines. (Fields: “Come up and see me sometime!” West: “I will…my little chickadee!”)
*To be pedantic, West’s catch phrase is a slight misquote from She Done Him Wrong.
In Blazing Saddles, Jim (Gene Wilder) tells how he gave up gunfighting when a six-year-old kid challenged him to draw. In Willy Wonka & the Chocolate Factory, when Willy is meeting the kids to come in to the factory, Mike Teevee (in western garb) draws on him.