Though I am just a man,
You may be quite a fan.
You may think I cannot die,
You may have seen my taxi fly.
Bruce Willis is a man, and as an actor he has lots of fans. He cannot die in Unbreakable and flew a taxi in The Fifth Element
Later I saved everyone,
I'll make you cry, even the sun.
Then suddenly I was dead,
Don't let that get to your head.
He saved everyone in the Die Hard films and in Tears of the Sun, which is what the 2nd line is referencing (Thanks @Spacemonkey). He turned out to be SPOILERS!! dead in The Sixth Sense.
I took some time, went back and forth,
Found great strength, and great worth.
Thought I could settle down,
That didn't work, just made me frown.
Bruce Willis went back and forth between different types of movies? Or maybe making/not making movies? And ended up not being happy if he wasn't filming? (I'm not 100% sure about this one)
I have many well known friends,
They think we can be thrown away, in the end.
Figure now who I may be,
And where you often see me.
He appears with many other well known action heros in The Expendables, but alas, he is not expendable. You're Bruce Willis! And I often see you in these films.