Any time a group of actors, singers or other celebrities gain fame or notoriety together, they're called "The [word that rhymes with rat] Pack"; viz., Brat Pack, Frat Pack, Eli Roth's "Splat Pack", etc..
The original Rat Pack was a loosely defined group of actors (and a few actresses) that sprang up in the Fifties, centered on Humphrey Bogart. According to long-standing Hollywood legend, Bogie and his buddies (David Niven, Sid Luft, Cary Grant, et al.) came home around dawn after a hard night in Las Vegas, and Bogart's wife, Lauren Bacall, said, "You look like a goddamn rat pack!" Among those original rats was Frank Sinatra, who took over as pack leader upon Bogie's death in 1957. Shortly, Dean Martin and Sammy Davis Jr. would join, and when Peter Lawford and Joey Bishop came on board, they had themselves a Rat Pack.
It is worth noting that Sinatra absolutely hated the term "Rat Pack", because he deeply resented being associated with rodents; instead, during his time in charge, he frequently insisted on using the terms "The Summit" or "The Clan" for the group instead.
The Rat Pack were legendary for their Las Vegas performances, which were seldom scheduled in advance. About the time they hit town to film Ocean's 11 in 1960, they started playing the Copa Room at the Sands, and scoring a ticket was like winning the lottery. Everybody who was anybody showed up, and audience members were frequently incorporated into the act. To give you an idea of how hard it is to publicize such an arrangement, at one point the Sands billboard proudly presented "DEAN MARTIN - MAYBE FRANK - MAYBE SAMMY".
The Rat Pack also campaigned actively for presidential candidate John F. Kennedy, whose sister was married to Lawford (thus Sinatra's nickname for him, "Brother-in-Lawford"). After JFK was elected, Lawford distanced himself from Sinatra due to the latter's supposed Mafia ties; that was a quick ticket out of the Rat Pack for him. By around 1970, the Rat Pack was unofficially disbanded.