Here's the Amazon page for Sylvia Nasar's book A Beautiful Mind, on which the film was (somewhat loosely) based. And, here's the film page.
An article by Nasar based on her book ran in the June 1998 issue of Vanity Fair magazine; unfortunately, the article is not available on line. What can found online (through Galileo -- "newspapers", "Lexis-Nexis", "general news") is Nasar's New York Times article on Nash that eventually grew into her book: "The Lost Years of a Nobel Laureate", NYT, Nov. 13, 1994.
Jim Holt's (sort of) "book review" in Slate (May 1998), both gives the flavor of the Nasar's book and notes that quite a few mathematical geniuses have been afflicted with mental illnesses.
Another (sort of) "book review" is in this pdf file from the Notices of the American Mathematical Society (November, 1998), in which John Milnor discuss both Nasar's book and Nash's contributions to game theory and other mathematics.
A different article in Slate (by Chris Suellentrop) discusses the many liberties that the makers of A Beautiful Mind (the movie) took with Nash's life.
One inexplicable liberty is the scene the film makers use to illustrate the development of the "Nash equilibrium". First, Nash didn't get the idea in a bar. More importantly, the behaviors described by the Nash character -- "we should all ignore the blonde" -- are not Nash equilibrium strategies. After all, if every other man ignores the "blonde", any one man can improve his situation by approaching her.
To learn more about the Nash equilibrium, and game theory in general, see Avinash Dixit's Game Theory Explained (which is part of the PBS site noted below). Roger McCain's academic site also explains the characteristics of a Nash equilibrium.
Going through Galileo, you can also find a short Los Angeles Times op-ed piece that both discusses the movie scene noted above and describes correct Nash equilibria: "How Many Blonds Mess Up a Nash Equilibrium?", by Bart Kosko, LAT, Feb. 13, 2002. [Responding letters to the editor in response appeared under the title "Writers Compete to Bag the Nash Equilibrium", LAT, Feb. 18, 2002.] Another take on the same issue (along with a discussion of why the film makers didn't try to get this right) shows up in a different LAT piece: "A Beautiful Whine Over Story of Nash's Genius", by Steve Lopez, LAT, March 24, 2002.
The significance of Nash's research (and some of the work that followed it) is described in the press release announcing the 1994 Nobel Memorial prize won by John Nash and two others (the movie neglected to mention that Nash shared the prize with Reinhard Selten and John Harsanyi). After the prize was announced, Nash supplied the Nobel Committee with a brief autobiography.
PBS is putting together a show entitled A Brilliant Madness; here's a description of the film, an interview with Nash, and an extensive list of further reading. [There's much more at the PBS site.]
60 Minutes also did a story in which Mike Wallace interviewed Dr. Nash. One aspect addressed was the alleged "whisper campaign" designed to prevent A Beautiful Mind from winning an Oscar.
My own minor contribution to promoting an understanding of strategic play was to point out the existence of a dominant strategy for some players (many of whom didn't use it) in the ex-MTV game show Singled Out.
Finally, here are three New York Times articles (which should be accessible through Galileo) that address Nash or the film: