George Reeves died, and the details of his death were immediately fashioned into legend. The newspaper headline read "Superman Kills Self," conflating the man with one of his roles. It was, of course, the role that defined his career, but he didn't necessarily want it to define his life. Nonetheless, to this day The Adventures of Superman has a devoted following, and the death of its star is still cause for speculation.
Part of the reason people still talk about it is the so-called "Superman Curse." Supposedly, if you're involved in the production of Superman television or movies, you're doomed. The Unexplained Mysteries (dot com) has a page devoted to the curse. The Superman Homepage offers a page of "common superman misconceptions" related to Superman, which includes sections on Reeves' death and on the curse. Lou Anders writes an article about it in The Man from Krypton: A Closer Look at Superman. The article is titled "A Word of Warning for Brandon Routh," and was written prior to Superman Returns. It's a curiously nonsensical article, which focuses far more on Keanu Reeves than one would think an essay on Superman should focus on a person who has never played Superman (his role in The Matrix notwithstanding). It does, however, have this little bit:
"...it can't be glossed over that it was this injury (to Christopher Reeve) which began the idle speculation that something supernatural existed called the Superman curse. Perhaps man isn't meant to reach too high, the thinking goes, and daring to take on the role of such a super man tempts the gods too much."
I'm tempted not to note here that Hugo Danner, protagonist of Gladiator and often-cited inspiration for Superman, died while tempting the "gods" by cursing them. He's struck by lightning.
Anyway, Greg Hatcher writes about George Reeves' death on Comic Book Resources.
Here's a page about George Reeves' ghost haunting the house where he died, which I don't think I'd encountered before.
The Straight Dope tackles the subject here.
There's a lot more to this. A book was written about it: Hollywood Kryptonite: The Lady, the Bulldog, and the Death of Superman. This book seems to have been the primary inspiration for Hollywoodland, a film that creates a fictional detective to investigate the case. The book pretty much goes for a murder verdict, the film concludes suicide. The book also goes over a lot of the rumors about Reeves.
There's so much more to this. The rumors persist. In her recent Memoirs of an Occasional Superheroine, Valerie D'Orazio writes about her contemplation of suicide: "Oh, how was I going to do it? Window. Sixth floor. I think George Reeves died like that, no? Took LSD, thought he was really Superman? or was that an urban legend?"
I could link to websites all day, but this seems to cover the important facets.