Who are some famous trumpet players?

Answer:

Oh, gosh, there are hundreds! Louis Armstrong was one. Randy Brecker, Maynard Fergeson (spelling?), and so many more. Louis Armstrong was one of the best :)
Legendary: Wynton Marsalis, Maynard Ferguson, James Stamp, Rafael Mendez, Thomas Stevens, Phil Smith, Adolf Herseth, Miles Davis, Lee Morgan, Freddie Hubbard, Clifford Brown, Dizzy Gillespie... and MANY MORE
Modern: Terrell Stafford, Wayne Bergeron, Adam Rapa, Chris Martin, Joe Burgstaller, Wynton Marsalis, David Hickman, Manny Laureano, Allen Vizzutti, Vincent Dimartino, ... so many more.
Nowadays, there are many more good lead players than there used to be, but far less soloists/ orchestral players. Though there is a new wave of young classical and orchestral talent coming from Europe and the states: Matt Muckey, Ruben Simeo, Sergei Nakariokov, as well as tons that I left out.

a few others are: Mike Vax, Arturo Sandoval, Doc Severson. I have heard many of them either in concert or in a clinic, just amazing what they can do. My one mistake that I will regret is missing Freddie Hubbard live. Also its hard to compare trumpet players of different times, Louis Armstrong was the best of his time, had a good voice also.