I beg to differ on this. There are some terrible character ideas:
1. Any character that goes against the assumed nature of the world that is being played in, and against the DM's guidelines-
Examples: Characters who have mysteriously come out of, say, 21st century earth and landed in, say, Middle Earth or the Forgotten realms are typically a bad idea. (Entire campaigns could be based around this, however, and it has been masterfully done in literature (Moorcock's Erekose is a good example), but it can wreck the flavor of a tightly constructed game).
2. Overpowered magical races that also spoil the game. A pile of half-fiends, half-celestials, half-dragons (what is with all these half-breeds, anyway), giants, minotaurs, and the like as PC's can not only throw off game balance if done improperly, it can be detrimental to low and mid magic settings as well.
3. Characters of conflicting alignments. I've pretty much banned evil characters from my games. I will allow them, but I strongly encourage neutral or good behavior. I play heroic fantasy.
4. Some ideas are just idiotic to begin with, even if they have an excuse. One guy I played with once made a Xaositect for a Planescape campaign who devoted his life to distributing chickens from his bag of holding- everywhere. We'd fight fiends- he'd hurl chickens. We met celestials- he'd give them a dead chicken from his bag. And that was all the stupid Githzerai did! He didn't fight, he didn't contribute to the party- he distributed chickens. It was quite aggravating to the DM (he was kicked out of our group after the third session) and cost a few PC's their lives.
Players can play whatever they want within reason, and the guidelines of the campaign.
If I sound like an iron-fist DM, I'm not. My players have played a diverse and interesting slew of characters, ranging from halfling necromancers bent on becoming vampire-liches to galaxy traveling pimps, from mysterious elven-raised wandering warriors to gnomish artificers with flying, fireball-launching mechanical constructs. I've DMed Dryad Druids, Voadkyn Rangers, Drow Assassins, Wookiee Mechanics and 12 year old Hackers. It takes all kinds- it just depends on the players and the campaign.