The Book of Mormon score is made up of parody songs. A lot of the melodies and ideas are taken directly from classic tunes (ex. I Believe/I Have Confidence or Sal Tla ka Siti/Somewhere that's Green or You and me (but mostly me)/The Wizard and I).
The show's fun and all, but I would hardly call it "original" or "brilliant."
Also, the opening vamp of "Tight Knit Family" from Falsettos always reminds me of "The Little Things" from Company (especially on the 2007 cast recording).
"A Little Fall of Rain" has always reminded me strongly of another song. But I haven't been able to place it. I wouldn't be surprised if it is a Jimmy Webb song because the melody has a very Webb feel to it.
The Boy Friend is supposed to be a parody/"pastiche" of 1920 romantic comedy musicals and I'm pretty sure one of it's biggest influences came from No, No Nanette. The songs are so similar. Not just musically but also lyrically. Like for example, "Sur la Plage" from the Boy Friend is exactly like "The Call of the Sea". The tempo, accompaniment are similar and they are both about the sea. "Sur la Plage" (a French phrase meaning like by the sea) is about a fun day at the beach and "The Call of the Sea" is about the sea brings joy and an air of romance to the character. Same applies to "I Could be Happy with You" from the Boy Friend and "I Want to be Happy" from NNN. Also, "Tea for Two" from NNN reminds me a lot of "Too Many Tomorrows" from Sweet Charity.
If a song sounded exactly the same it would be a matter for the courts All examples I've ever read are analogous to saying David Letterman and Santa Claus look alike.
Andrew Lloyd Webber often repeats his own melodies, as well as adapting classical melodies. "The Music of the Night" and "All I Ask of You" have similar note progressions. I'm not sure why he did this, since MOTN is the Phantom's love song, while MOTN is Raoul's.
I read about a crazy copyright case (which, if I'm not mistaken, got thrown out of court) in which the studio that owned the copyright sued the composer for violating the copyright in composing later songs that sound similar. What did they expect -- everyone has a signature sound.
Audrey, the Phantom Phanatic, who nonetheless would rather be Jean Valjean, who knew how to make lemonade out of lemons.
I believe the composer in question was singer-songwriter John Fogerty, who had been lead singer-songwriter of Creedence Clearwater Revival. He was accused of plagiarizing his old band's sound, when he had been the primary creative of the band in general.
A couple I always mention: The bridge of the "Kiss Me" quartet in ST is eerily the same as TV's "Dynasty" theme. And ALW's main motif in "Whistle Down the Wind" was proven to be the John Williams majestic theme from "Jurassic Park" and I believe ALW subsequently cut the song. If anyone knows the wonderful film comedy "Starting Over," Marvin Hamlisch brazenly borrowed two defining runs from "What I Did For Love" for the recurring theme.
"I'm a comedian, but in my spare time, things bother me." Garry Shandling
And ALW's main motif in "Whistle Down the Wind" was proven to be the John Williams majestic theme from "Jurassic Park" and I believe ALW subsequently cut the song.
I think the song you mention is "The Vaults of Heaven," the first song in the show. In the original DC production, the melody for the words "open up the vaults, open up the vaults" did indeed sound just like a prominent theme from Jurassic Park. He changed the melody a bit for London so it's not so dead-on.
Regarding "If Only You Would Listen" from School of Rock, I did notice the similarity to "Someone Else's Story." I think it's basically limited to one measure, but that measure is exactly the same and it happens to contain the title of both songs, so it's fairly prominent. The same song also has a few bars borrowed from the title song of The Beautiful Game.
Nowadays every time I listen to Learn your lessons well from the 2011 Godspell revival I always think it's gonna start with 'Jack and Jill went up the hill'. So I'd say the beginnings of Naughty from Matilda and Learn your lessons well are very similar.
Today I discovered another ALW steal, not from the theatre world but the pop one.
The beginning and in-between verses melody of "Another Suitcase In Another Hall" is stolen directly from the same components of the 1967 Lemon Pipers song "Green Tambourine," except maybe the final note of each phrase.
This may not exactly answer the question, but there are times when I hear a composer add a new song to a previous work that sounds out of place, sometimes because it sounds like whatever show they were writing at the time. Sondheim's "Country House" from the '87 London production of Follies sounds straight out of Into the Woods, at least musically, to me. Similarly, "Something Just Broke" sounds like it belongs in Passion and not Assassins.
The first time I heard The Prom, I thought "Unruly Heart" was a mix of "You Will Be Found" from Dear Evan Hansen, "I Am What I Am" from La Cage Aux Folles, "Can I Close the Door" from Motown, and from outside the theatre canon, "A Moment Like This" by Kelly Clarkson and "The Wind Beneath My Wings" by Bette Midler. Not exactly similar songs, but they all have near-identical song structures.
A slightly different answer since it's all the same composer, but if you listen to "Miracle Song" in Anyone Can Whistle, it has some similarities to "The Ballad of Czolgosz" from Assassins, and is also copied more directly in "Gold!" from Road Show. Actually, quite a lot of Road Show seems to have an Assassins touch to it, and Sondheim has definitely reused snippets of his own melodies here and there quite a bit, though he's not the only one (Alan Menken, Andrew Lloyd Webber, etc.)
The instrumental of "Counting Down to Christmas" from A Christmas Story sounds just like the instrumental from "Mr. Witherspoon's Friday Night" from Lucky Stiff.
Same with the prologues of Passion and Parade. Not identical, but similar structure. A solo snare drum, then a boom of the full orchestra, then a clarinet figure.
For some reason, I realized "I Am Unworthy of Your Love" from Assassins and "Only Us" from Dear Evan Hansen have similar structures, even in the key changes and switches between singers. It's one character with the first verse and chorus, then a key change into the other character singing the second verse and a partial chorus, then a bridge that involves alternating lines and some together lines, then a final chorus in a new key with both characters singing together.
"I think that when a movie says it was 'based on a true story,' oh, it happened - just with uglier people." - Peanut Walker, Shucked
Last year I saw a musical called Severa in Lisbon, and while it was meant to be a brand new original musical it contained snippets of the score from Martin Guerre, orchestrations more or less intact. The most brazen was Martin Guerre's title song, which had whole verses and choruses lifted. That one actually appears on Severa's cast recording, with the track credited to Filipe La Féria.
When I told my friend, she shrugged and said Filipe La Féria was Portugal's Andrew Lloyd Webber.