Throughout history we have seen some common similarities among famous, successful musicians. I have broken them down into four main characteristics that I believe make for a successful musician. Keep in mind that not ALL famous musicians have each and every one of these traits.
The first and most obvious, is musical skill and artistic ability. In order to create music that people will enjoy, there must be a point along the line where there is some musical influence behind a piece of music; whether it be the skill of the actual musician or the skill of the audio technicians making that perfect adjustment to the auto-tuned vocals. In simple terms, there has to be something that makes the music sound good.
Next, a musician should have charisma, generally referring to their performance on stage. Charisma is something that words cannot really explain, but its something that when a musician performs it creates a certain vibe that rattles the emotions of the audience. Charisma normally varies among artists, and the vibe created normally depends on the type of music. But in all forms of music, charisma is what drives people through the doors of the concert hall.
Appearance... although we'd like to think music is all about the art, the truth of the matter is, it isn't. The person that fans chase around the streets has to have some signature style that is recognizable among the public. Appearance creates character, from Jimi Hendrix's extremely exotic clothing, to Johnny Cash's strictly black wardrobe, and Bono's signature shades, every musician should have an iconic appearance that people will identify with only that person.
The last characteristic doesn't have much to do with music, one that all famous people must have. The ability to live as a celebrity, or attitude, determines the lifespan of a musician's career. Some musicians have been performing for decades; like Bob Dylan who has played since the 60's and is still performing today. On the other hand, some musicians just can't handle the lifestyle of being famous, and normally end their career by doing something stupid; like Justin Bieber, who went on a rampage of bad decisions and practically lost the majority of his fan base.
These are the characteristics that I believe make a successful musician. Very few actually have all of these, but the ones that do are usually the ones who make the biggest impact on music.