In Psycho III, Anthony Perkins (as Norman Bates) plays a sad, contemplative theme on the piano, and it happens to be a variation of the main title of Carter Burwell's score.
In The High and the Mighty, John Wayne's character frequently whistles a tune that is the film's main theme.
BSG, Bear's theme for the final Cylons helps Starbuck steer the Galactica towards our lovely blue planet:
Here's an earlier scene (with some annoying embellishments by whoever uploaded it) where she first remembers the theme. Probably my favorite scene of the series. It was great to see the music play such a pivotal role!
Two nice examples: In "Walk, Don't Run" Cary Grant whistles the Main Theme from "Charade" while he tries to make coffee.
And a special one which is very hard to hear (I found it while making my final University examination about the cultural references in the Bond movies). It's a nice inside joke from the sound guys from "License To Kill" during the final truck chase: while the bad guys shoot on the truck in which Bond is, you can hear that the sound of the bullets are making a part of the Bond melody...
On Boston Legal, Jerry Espenson, played by Christian Clemenson now playing Medical examiner Tom Loman on CSI Miami, Jerry sings the theme from the show. There are other references during the run of the show. I recall at one point either Denny Crane or Alan Shore saying "cue the music" or something like that right prior to the theme playing. I miss that show.
Jack Black's character in The Holiday is a film composer, and there's a scene where he's in a Blockbuster with Kate Winslet, and he hums her some classic tunes. One of them is Hans' Driving Miss Daisy, so it's not exactly referencing its own score, but it's referencing its own composer!
Don't forget a couple of famous Mel Brooks examples: BLAZING SADDLES - Duke Ellington and his band are revealed to be playing Cleavon Little's entrance music in the desert. HIGH ANXIETY - As we hear the music from Psycho on the soundtrack, a bus drives by with the LA Phil on board playing the music.
As the opening titles begin we hear Holland working on his piano playing the main theme of his symphony. A few missed notes here and there as he tries to figure out where the piece is going. Then Kamen's orchestra kicks in a takes over as Holland air conducts to the music in his head.
On Boston Legal, Jerry Espenson, played by Christian Clemenson now playing Medical examiner Tom Loman on CSI Miami, Jerry sings the theme from the show.
I could be wrong but doesn't Val Kilmer turn on the radio at the end of the film and they briefly play the Saint Theme before Roger Moore comes on?
It's just before that. He drives by the Scotland Yard guys, who have mistakenly tackled the wrong man, and honks his car horn at them, and the horn plays the Saint theme.
There are other good Mel Brooks examples. In "High Anxiety" the song Brooks' psychiatrist character croons in the nightclub Sinatra-style is the main title theme with lyrics added. In "Young Frankenstein" the music which calms the beast at the end is that score's main theme on solo violin (with Marty Feldman providing a French horn obligato). In "Spaceballs" the big Transformers-like ship transformation into "Mega Maid" ends with a dramatic kettle drum finish. The drum solo is discovered to be performed by one of the ship's crewmen.
Going by memory here, but don't the characters in I'm Gonna Get You Sucka make reference to their own theme music? I seem to remember one character walking the streets with his own band playing his Shaft-like theme music, marching behind him.
