Well, let's see...
Are we talking Movie characters? If so then:
Aragorn, because I hate his crown/sword/confidence mix-ups
Legolas (attracts too many fangirls)
Gimli (no comic relief in MY middle-earth)
Merry and Pippin (see previous reason)
Arwen (She killed Glorfindel
)
Denethor (he's too psycho, too soon. Besides, what happened to his chainmail?)
Faramir, because he turned to the dark side....
That big Uruk, what's-his-name, the one who kills Boromir..... (Can't abide additional characters when you cut out so many real ones)
And I know this makes 11, but Merry and Pippin are small, so I'll chuck out Celeborn too. Whatever happened to the fearless Sinda prince, and Galadriel's partner/equal?
Now, if we're talking book....
Glorfindel (he's good at dying. Did it once in Gondolin, and again for the movies)
Goldberry. WHAT purpose does she serve in the plot? Besides, she makes it rain..
Gloin: Dwarves in a boat? Come on, not everybody's a Gimli.
Ted Sandyman: Never got his comeuppance in the book. It's about time!
Radagast: He didn't do his job. He's got to stay and finish it.
Gollum: Schitzophrenic, ugly, greedy, lived-WAY-too-long, almost-naked little bugger. Need I say more?
Cirdan: SOMEONE has to stay behind and make sure Radagast gets a ride later...
Sauron: He's just plain unpopular. Besides, the last time he took a boat ride, he sunk the island.
The Mouth of Sauron: Bad credentials, hangs out with orks, works for Sauron. The guy's practically a BUREAUCRAT, for Aman's sake!