As a DM, I haven't had to eject a problem player from my games. As a player, there was one incident... and I'm not very proud of how it happened.
The group in question was playing a very long-running 2nd edition D&D game, with a large number of players (at that time 9 + the DM, IIRC). One player (who we'll call Carrie) started playing because she was the girlfriend of another player, and was jealous of the time her boyfriend spent gaming. The group met at my house, since I had the most room and a large table.
After they broke up, both continued to play with the group. Carrie was rather bitter about the breakup, and continued to belittle her ex with snarky side-comments. It became apparent that she was only playing because a few other players were taking her out to bars after the games.
As time went on, she contributed less and less to the actual game. She started taking paralegal classes, and brought her homework to the games. When she wasn't trying to do homework at the table, she was playing with her cell phone. A few times, she even napped at the table. This behavior continued for months.
Things came to a head one night when the party was facing a major battle. While the rest of the players were planning how to approach the situation, Carrie was sleeping with her head on her homework. Just as we were finalizing our plans, she woke up and said something like "@#&%* it, aren't we ever going to do anything tonight? Stop talking and play!"
At that point, I lost my temper. I really don't remember what I said (although I do know I refrained from swearing), but it went something like this:
"You know exactly how we play this game. You haven't been paying attention or participating at all... you've been asleep! If you want to play, PLAY! Don't take up space and be disrespectful to everyone else!"
Her response was something like "*&#% you, I don't have to take that &#^@! I'm outta here!" She packed up her things and left. No one else said a word.
I appologized to the rest of the group for HOW I confronted her, but not that the confrontation happened. I shouldn't have lost my temper with her, but I'm glad she left.
If something like that ever happened again, I would say something earlier and in a more controlled way.