This article is from the X-Men Comic Books FAQ, by Kate the Short (email@example.com) with numerous contributions by others.
In 1963 (our time, not Marvel time), Professor Charles Xavier gathered
together a group of five young mutants to help them train their powers.
He also hoped that they could help protect innocents from "evil
mutants," as well as do good deeds for the rest of humanity. This group
was called the X-Men, after the eXtra-powers that each member possessed
(the resemblance to Xavier's last name was not entirely coincidental).
This original team consisted of Cyclops (Scott Summers), Marvel Girl
(Jean Grey), Iceman (Bobby Drake), Angel (Warren Worthington III), and
the Beast (Hank McCoy). The book was written by Stan Lee and pencilled
by Jack Kirby. Magneto was the villain of the first issue, and his
fiendish plot was to terrorize a missile base to prove how tough he was.
Havok (Scott's brother Alex) and Polaris (Lorna Dane) were semi-regular
members who later joined the team. Mimic (Calvin Rankin) was briefly a
member, and Changeling pretended to be Professor Xavier for a while.
The original X-Men title was "cancelled" after 66 issues, due to low
readership. It became a reprint title, reprinting original stories it
had shown only a few years earlier, while the X-Men went to supporting
roles in titles like Amazing Adventures and Ka-Zar Quarterly.
This all changed with the introduction of the "new" X-Men in Giant-Size
X-Men #1, which came out in 1975. Written by Len Wein and penciled by
Dave Cockrum, it had the original team captured by the Living Island of
Krakoa, who manipulated Xavier into bringing together a second team of
mutants to help feed its unholy hunger: Nightcrawler (Kurt Wagner),
Wolverine (Logan), Banshee (Sean Cassidy), Storm (Ororo Munroe), Sunfire
(Shiro Yoshida), Colossus (Piotr Rasputin), and Thunderbird (John
Proudstar). This new team succeeded in rescuing the old heroes, and most
of the new recruits stayed on to form the team that would make the X-Men
comic book legends. The title restarted with X-Men #94, with Chris
Claremont taking over for a sixteen-year run as writer. Soon after,
Thunderbird died and Sunfire quit, while Angel, Jean, Iceman, Polaris,
and Havok left the team on good terms. Soon afterward, Jean Grey joined
the infamous shuttle mission and "died", and Phoenix entered the picture
in X-Men #101. X-Men became The Uncanny X-Men with issue #114.