This is fairly interesting. /Film interviewed Academy Award-winning screenwriter Eric Roth about his latest film The Curious Case of Benjamin Button, and Roth revealed that he had actually completed a version of his Forrest Gump sequel, but he, Hanks and Zemeckis shelved the project due to 9/11:
“I turned in my version of the Forrest Gump sequel, or Part II, whatever you call it… It’s a continuation really — I want to start the movie literally two minutes after the end of the last one, with him on the bus bench waiting for his son to get home from school. But I turned in the script the night before 9/11. And we sat down, Tom [Hanks] and Bob [Zemeckis] and I, looked at each other and said, we don’t think this is relevant anymore. The world had changed. Now time has obviously passed, but maybe some things should just be one thing and left as they are.”
Author Winston Groom wrote a follow-up novel titled Gump and Co. that was released in 1995 and its content is quite intriguing (via /Film):
[The novel] follows Forrest as he stumbled through important US events in the 1980s and early 1990s. According to Wikipedia, Gump plays football for the New Orleans Saints, sells encyclopedias door-to-door, works on a pig farm, and helps develop the infamous New Coke. He accidentally crashes the Exxon Valdez, helps destroy the Berlin Wall, fights in Operation Desert Storm and meets many celebrities along the way including: Colonel Oliver North, the Ayatollah Khomeini, John Hinckley, Jim Bakker, Ivan Boesky, Ronald Reagan, Saddam Hussein, Bill and Hillary Clinton, and Tom Hanks.