I begin:

1. Beethoven
2. Elvis
3. Bach
4. Beatles
5. Mozart
6. Michael Jackson
7. Madonna
8. Rolling Stones
9. Tchaikovsky
10. ABBA

More?

gucci mane

I can confidently say Elvis was not one of the greatest musicians of all time. Or Michael Jackson. Or Madonna. Or Abba, The Rolling Stones, or the Beatles (ok maybe George was top ranking at the guitar... and maybe in a certain light he may be considered the best...you got me there). I can't comment on the others as they were dead before there was any way to record them performing.

If we were discussing composers on the other hand.... (and even then, not Elvis or MJ)

http://www.thefreedictionary.com/musician
"One who composes, conducts, or performs music, especially instrumental music."
I presume this is the definition intended.
Also, Elvis most definitely must be there he kicks ass! Not sure about ABBA, they have no staying power, they will be forgotten soon. Elvis is going to be around for a long time

Something along those lines, yes. And the vocals, and the show.

Rogers and Hammerstein were the greatest.

The Sound of Music

Flower Drum Song

Cinderella

The King and I

South Pacific

State Fair

Carousel

Oklahoma!

These aren't songs. These are entire plays/movies that all have great songs in melody and lyrics.

justin bieber

Rebecca Black beats Bieber.

I have a hunch this thread will not go the way I intended. The subjectivity of course rules, as when it comes to art. Maybe we should talk about the most influential musicians...

Thread title should be "greatest musicians of their time" imo.

The list for equally important classical musicians would hold at least 15 names alone.

There is single bands who had major influence on a whole generation, yet there is arguably bands of the time who were much more talented/artistic.

Bob Dylan.

Roger Waters
Black Sabbath

[I do like ABBA and Mozart being listed together in the OP, bit unfair on the Rolling Stones]

AC/DC

This. The thing that made Elvis so polarizing was that he was effectively a white man singing and performing black music. Up until he came along, black artists were obviously targeting the white middle-upper classes who were the predominant purchasers of music, the problem was they didn't buy these records (or, at least to the volume that they did once Elvis hit the scene) more or less because the artists were black. Once Elvis cornered this market, he began covering song after song, giving them the rockabilly swing and sound that we most associate with him. Elvis is undoubtedly one of the greatest performers of all time, and also one of the most influential because of the cultural explosion he helped fuel. I definitely would not classify him as one of the greatest musicians of all time, however, his total number of original compositions was very, very small.

This being said, I think I'm going to lock this thread (perhaps only temporarily) because I do think there are a lot of great and interesting debates and discussion that can emerge when looking at the history and evolution of music in a variety of different contexts, but I fear that the approach this thread takes is going to lump too many artists and eras together which isn't really going to accomplish anything because of what the OP said regarding the extreme subjectivity when asking a question such as "Who are the greatest musicians of all time?" I'm going to try and think of some alternatives that we can explore to get this discussion going, will post results soon.