The Babylon 5 Curse is the observation that several of the main cast of Babylon 5 have died, often around age 60, well before the American life expectancy of 78 years. Granted, you get any group large enough and statistically you're going to have a few who die early, but it's unusual that so many of the main cast have died decades before average.
The likely explanation is that it's the result of some sort of sampling bias. The show was made in the mid to late 90s, when smoking was a more acceptable vice. The CDC estimates that smoking reduces life expectancy by at least 10 years, which matches well with the deaths of several of the actors. Actor Andreas Katsulas, for example, died of lung cancer in 2006, a direct result of his passion for smoking. Likewise, a lifelong struggle with drug abuse played a role in Jeff Conaway's death from pneumonia. Others have died from more random causes--Richard Biggs, who portrayed Dr. Steven Franklin, died suddenly at age 44 as the result of an aortic dissection.
The most noteworthy victim of the 'curse' was Michael O'Hare, the original male lead. O'Hare left the show after the first season due to paranoid delusions and in inability to distinguish between reality and the world of the show. Though treatment was somewhat effective, he never fully recovered and it forced his retirement from acting. He later died of a heart attack at age 60.
At the moment, few of the series regulars have defied the pattern. Walter Koenig--best known as Pavel Chekov from Star Trek--is currently 79 years old. Efrem Zimbalist Jr., who had a recurring role in the fourth season, lived to be 95 (though he was already in his late 70s when cast). Actors Louis Turenne and Damian London have both lived into their 80s, however their roles were fairly minor.
With the majority of the main cast still in their 50s and 60s, it remains to be seen if the pattern will continue. In the show, lead character John Sheridan dies and is resurrected but is limited to 20 more years of life. In a macabre way, it seems this tragic flourish is playing out on the entire cast.
Richard Biggs Aortic Dissection May 22, 2004 (aged 44)
Andreas Katsulas Lung Cancer February 13, 2006 (aged 59)
Jeff Conaway Pneumonia May 27, 2011 (aged 60)
Michael O'Hare Heart Attack September 28, 2012 (aged 60)
Jerry Doyle Unknown July 27, 2016 (aged 60)
Recurring Guest Stars
Tim Choate Traffic Accident September 24, 2004 (aged 49)