Gwaihir - Oh, that eagle guy? Meh. He'd've been more famous if he'd flown to Mordor and dropped in the Ring and saved Frodo the trouble of walking there. :P
Tol-in-Gaurhoth - ...nicely done, sir.
Mordor - You mean that place that's not Angband?
Feanor - Fairly good.
Bard - Decent, but not, I'd say, quite up to the level of Feanor, the other submission in the 'famous *people* category.
Great Goblin - He himself is not so very famous outside of his caves, I'd say.
Shadowfax - Not famous necessarily, though he ought to be.
Two Trees of Valinor - Again, glorious, but not necessarily famous.
The Prancing Pony - There are more famous pubs, but I do like the idea behind the submission.
Turin - Again, decent, but eclipsed by Feanor.
Glorfindel - He wasn't even famous enough to make it into the movie.
Elrond - Yeeeeeeeeees....but not so much as Feanor.
So, for me, it's between the funny, Downsian play (Tol-in-Gaurhoth), the real, famous person play (Feanor) and the funny Tolkieny play (The Prancing Pony). I'd be open to people making arguments for why the other four characters who rival Feanor should be chosen instead of him, with more likelihood of success going to Turin or Elrond.