The basic plot and characters are based on LA BOHEME so no, RENT cannot be considered original.
LIGHT IN THE PIAZZA is based on an Elizabeth Spencer novella, which subsequently became a movie.
As for Sondheim, COMPANY is based on a series of one acts by George Furth that were unpublished and unproduced -- he took them to Hal Prince who thought they might work better musicalized and introduced him to Sondheim -- so it's, for all intents and purposes, original. ANYONE CAN WHISTLE, FOLLIES, PACIFIC OVERTURES, and SUNDAY IN THE PARK WITH GEORGE are more or less original (though the latter two were inspired by historical events and a painting, respectively). Much of the plot of INTO THE WOODS is original (The Baker Story is an invention by Lapine, as are Rapunzel's Princes and all of Act II). For ASSASSINS, one could argue that while characters are based on historical record, the plot of it is original (obviously none of these people ever actually met each other).
Other "original" shows not mentioned so far:
--ALLEGRO and ME AND JULIET (two of only three Rodgers & Hammerstein shows that weren't hits)
-- OF THEE I SING
-- ANYTHING GOES
-- BRIGADOON
-- FINIAN'S RAINBOW
-- HAIR (though the book consists of loosely connected vignettes)
-- LADY IN THE DARK
-- FUNNY FACE
-- CALL ME MADAM
-- REDHEAD
-- BYE BYE BIRDIE
-- ON THE TOWN
-- BELLS ARE RINGING
-- NO STRINGS
-- ON A CLEAR DAY
-- HALLELUJAH BABY!
-- GREASE
-- PIPPIN (not really based on the story of Pepin)
-- THEY'RE PLAYING OUR SONG
-- DREAMGIRLS (not really based on the actual story of the Supremes)
-- CITY OF ANGELS
"What a story........ everything but the bloodhounds snappin' at her rear end." -- Birdie
[http://margochanning.broadwayworld.com/]
"The Devil Be Hittin' Me" -- Whitney