The band originally consisted of vocalist Axl Rose, lead guitarist Slash, rhythm guitarist Izzy Stradlin, bassist Duff McKagan, and drummer Steven Adler. Their albums Appetite for Destruction and G N' R Lies are credited by many for "saving" rock music after the rise of disco and pop. Matt Sorum replaced Adler on the amazing double-album Use Your Illusion I and II.
Many reasons led to the break-up of the original band. Izzy quit and was replaced by Gilby Clarke whom Axl would later unceremoniously fire without consulting the rest of his bandmates. Guns N' Roses' next album, The Spaghetti Incident?, was a critical and commercial disappointment, and it included a controversial cover track of a song written by the infamous Charles Manson. After recording a cover version of The Rolling Stones' "Sympathy for the Devil" with Paul Huge on rhythm guitar for the movie Interview with the Vampire, Slash quit and was replaced by Robin Finck. Axl Rose then fired Sorum and eventually Duff left the band too, leaving Axl as the sole original member.
Although the band never officially "broke up," the new version of Guns N' Roses (Axl Rose, Ron "Bumblefoot" Thal, DJ Ashba, Richard Fortus, Tommy Stinson, Frank Ferrer, Dizzy Reed, and Chris Pitman -- and others, including Brian "Buckethead" Carroll) has been viewed by some fans as a pale imitation of what it was. The long-awaited new album Chinese Democracy was welcomed enthusuastically by many loyal fans, but failed to meet industry sales expectations.
The other original G N' R musicians have moved on to other things in their careers, including solo albums. Slash, Duff, and Sorum formed the supergroup Velvet Revolver with Scott Weiland and Dave Kushner.
I think the personality clashes might never allow the original Guns N' Roses to reunite longterm, but it would be nice to see them all get together on stage at least one more time for a song or two. Stranger things have happened.