The refrain of Blazing Saddles is clearly based on the refrain to the hymn "Yes, Jesus Loves Me"
Likewise, the chorus of Twisted Sister's We're Not Gonna Take It is (admittedly) derived from the Christmas hymn O Come All Ye Faithful.
Twisted Sister did a cover of "O Come All Ye Faithful" that sounds almost identical and even used a few of the same guitar riffs.
Several places in the soundtrack of Titanic, such as at 0:50 of Southampton, and the entire soundtrack of composer Joel Mcneely's Disney's Iron Will is suspiciously similar to Stephen Foster's classic song "Jeanie With The light Brown Hair".
The song "Let's All Sing Like the Birdies Sing" in Disneyland/Disney World's Enchanted Tiki Room is suspiciously similar to Offenbach's "Barcarolle" from The Tales Of Hoffmann (also called "Belle Nuit" from Les Comtes d'Hoffmann).
Several parts of James Horner's Stealing The Enterprise, Battle In The Mutura Nebula, and Genesis Countdown in Star Trek II and Star Trek III was later reused in his own score for the The Rocketeer and parts of the score was reused in Walt Disney World's Fountain of Nations in Epcot.
The Phantom Menace uses a knockoff of the third movement of Dvorak's ninth symphony in the lightsaber battle at the end.
John Williams has done it before; the Imperial March from The Empire Strikes Back (and just about every subsequent movie in the series) is suspiciously similar to Chopin's Funeral March, with elements of Gustav Holst's Mars: Bringer of War movement from The Planets (the metre is changed and the order of the themes is mixed up a bit, but the similarities are fairly striking).
Especially during the Battle of Yavin, which also interpolates part of Jupiter: The Bringer of Jollity during the "X Wings Draw Fire" segment.
The main motif of the Ewok theme sounds a lot like the March from Prokofiev's "Love for Three Oranges".
"Augie's Great Municipal Band" music in the same movie is suspiciously similar to "The Emperor" music in Return of the Jedi. Part of the "A New Hope" music in Revenge of the Sith is suspiciously similar to of "Hedwig's Theme" from the Harry Potter series.
Although in the case of the former, that's the whole point. It's intended to invoke the Emperor's theme, the newly-elected Chancellor Palpatine being the Emperor and all.
"Make 'Em Laugh" from Singin' in the Rain bears more than a small resemblance to Cole Porter's "Be a Clown", which had appeared a few years earlier in MGM's The Pirate.
Gone with the Wind uses a Suspiciously Similar Song to Offenbach's "Galop Infernal" (or "The Cancan Song") in a restaurant Scarlett and Rhett visit when on their honeymoon - for some reason, since it's a public domain song (and probably was even back when it was filmed).
Tara's theme from the same movie also sounds a tad like Debussy's "Clair de Lune".
The rape/seduction scene in Akira Kurosawa's Rashomon is set to music that sounds suspiciously like Ravel's Bolero. The composer claimed he wanted to create something that sounded more original (and more appropriately Japanese) but Kurosawa kept pushing him back towards Bolero.
The "Stairway to Heaven" scene from Wayne's World uses a Suspiciously Similar Song in the home video version. In the original theatrical release, they used the actual "Stairway" intro.
The cultists performing a human sacrifice in Young Sherlock Holmes (not to be confused with the otherSherlock Holmes movie with cultists performing a human sacrifice) chant a song which also rips off "O Fortuna".
In the movie adaptation of Ghost World, the character Doug blares some heavy metal from his car stereo - it sounds a lot like an instrumental knockoff of Metallica's "Master Of Puppets".
In David Lynch's film of Dune, the scenes set on Caladan are scored with ambient string music that sounds a lot like the first movement of Dmitri Shostakovich's 11th Symphony, although the resemblance may not necessarily be intentional.
Speaking of Hans Zimmer, the soundtrack from The Rock is very similar to the score from Pirates of the Caribbean: Curse of the Black Pearl. (For those not in the know, Zimmer worked on both).
Zimmer is notorious for composing similar-sounding themes, mostly because he favours a standard "action movie theme" rhythm and chord progression. This also affects his slower pieces. Time from Inception does sound an awful lot like Tennessee from Pearl Harbor. Lots of the score from Gladiator also seems to turn up in the Pirates of the Caribbean films, similarly with King Arthur and Pirates again.
The opening credits music for WarGames is a slightly tweaked version of the overture to Georges Bizet's opera Carmen.
Sesame Street uses the unmodified tune of Fugue no. 2 for the "Monsterpiece Theatre" theme: "ABCDE, EFGHI, HIJKLMN, O-oP...."
The fight theme from the unreleased The Fantastic Four by Eric and David Wurst is basically John William's "Here They Come" from Star Wars. While the Theme song is more or less shades of "the Main Theme" from Jurassic Park.
Somewhat averted in the DVD release of Where The Buffalo Roam, as the new songs don't sound anything like the ones used in the original movie. Still pretty lame, though.
We couldn't / get the rights / to the real / song / so we had / some dude / write / this one / but we / had to / put him / in the / movie. / Here he is. / (shot of crowd scene with one person in the background circled) Totally/ Worth It
The opening credits to Freddy's Dead: The Final Nightmare features music that sounds very similar to "Night On Bald Mountain" by Modest Mussorgsky. Almost to the point, that you'd swear it actually was "Night on Bald Mountain."
In the Film Casablanca, the original script called for the two dueling anthems to be La Marsaillaise, the French National Anthem, and Das Horst-Wessel Lied, the official anthem of the Nazi Party, and the second part of the National Anthem of Germany after the Deutschlandlied / Deutschland Ueber Alles. However, Warner Brothers intervened, pointing out that Horst Wessel was at the time under the copyright of the Nazi Party. If the movie were only being screened in Allied nations, it would not have been an issue (as the Allies weren't interested in upholding the IP of a nation that was doing its best to destroy them), but as the film was also going to be distributed in neutral nations, where Germany could cause legal headaches for Warner Bros, they asked that the song not be used. In the film as finished, they used the similar in theme and sound Die Wacht Am Rhein, a 19th century song (which, for obvious reasons, had nothing to do with the Nazis).
Deep Blue Sea includes a suspiciously similar version of Madonna's "La Isla Bonita".
In the Heat of the Night has a scene where a character dances to a novelty-ish tune called "Fowl Owl on the Prowl", which sounds more than a little like Sam the Sham's '60s hit "Li'l Red Riding Hood". This was no accident, as the filmmakers actually wanted to use the latter song but couldn't get the licensing.