The screenplay for Forrest Gump comes to us from a guy named Eric Roth, who also co-wrote the screenplays for The Insider, Munich, and The Curious Case of Benjamin Button. That's quite a resume, Mr. Roth.
Roth adapted the screenplay from the 1986 novel by Winston Groom, although the move isn't going to win any awards for fidelity to the book. In the book, Groom focuses more on Forrest's adventures, while the movie spends a lot more time talking up Forrest's love for his childhood sweetheart, Jenny.
In director Robert Zemeckis' view, that focus makes Groom's book colder and more cynical than the movie. (Well, he would say that, wouldn't he?) (Source)
There was actually quite an un-Forrest-Gump-like conflict over the film at one point as Groom thought he was cheated out of money after Paramount Pictures argued that Forrest Gump didn't make a net profit. That's a hard argument to make when a movie grosses over $677 million, so the company eventually settled the issue by paying Groom more than $1 million for the rights to the book's sequel, Gump & Co. (Source)
But, don't look for Forrest Gump II: Gump & Co. to hit the big screen anytime soon. It's probably a good thing Paramount eventually tabled that one.