When it comes to music done for movies based on, or inspired by, classic and well known stories, I think you would be hard pressed to find a composer who has done more than Danny Elfman.
His portfolio of movies based on books for which he composed the soundtracks, or at least developed the main themes for, includes:
Scrooged (1988) – an updated version of Dicken’s A Christmas Carol
Black Beauty (1994)
Sleepy Hollow (1999) – a decidedly different interpretation of Washington Irving’s Legend of Sleepy Hollow
Planet of the Apes (2001) – which version was even more removed from the Pierre Boulle’s original book than the 1968 version
Charlie and the Chocolate Factory (2005)
Charlotte’s Web (2006)
If you allowed a couple of more contemporary author’s works in to this list, these would also count:
Meet the Robinsons (2007) – based on William Joyce’s children’s book A Day with Wilbur Robinson
Dolores Claiborne (1995) – from a Stephen King novel
Then, if you were to include well known comic book characters, the list grows with:
Batman (1989)
Dick Tracy (1990)
The Flash (1990) – actually a TV series that Elfman did the theme music for
Batman Returns (1992)
Spider-man (2002)
Hulk (2003)
Spider-man 2 (2004)
And while this doesn’t even complete his musicography, he did these movies which are also based on stories that originated in comics – Darkman (1990), Men in Black (1997), Men in Black II (2002) and Hellboy II: The Golden Army (2008).
Edward Scissorhands (1990) and The Corpse Bride (2005), are two movies which could just as easily be included in this list as the first has shades of Frankenstein, and Beauty and the Beast, and the second is loosely based on a Russian-Jewish folktale.
Lastly, if you wanted to stretch this list you could add the theme for The Simpsons TV series (1989+), which after 20 seasons and a movie is on its way to becoming an institution of its own (besides, The Simpsons has probably spoofed more classic and well-known books, movies and fictional characters then any other current series.)
