The Cure is considered to be one the most important musical acts of the 1980s, and have had much influence on musicians of today. And they are still an active band. They're often "accused" of being a goth band, which is not really true.
The master-mind behind the band is the singer Robert Smith, who writes all lyrics and almost all the music. They have existed since 1976 and has to date released 13 proper full length studio-albums, everyone with it's own style. They never sound the same on two records, although you can always hear that it's cure (partly because of Smiths characteristic voice).
Next album is hopefully released 2003.