I am a firm believer in making sure the players are happy with their PCs. These are characters that (barring total disaster) may very well be with them quite literally for years! If I can't give a player what he wants, then I will work with him to try and find a compromise that meets him partway.
In other words, I make sure that if I'm going to take on the responsibility of running a campaign, I'm going to make every effort to do it right. Part of that, to me, means being as involved in character generation as my players. If a player wants something exotic, I say "Okay, let me take a look at it." I take the time to examine it, decide if it's reasonably close to balanced, and if so I allow it--with the caveat that if I discover later that there was something I had missed, the player will have to be open to balance changes later.
This method has worked very well for me so far.
I have a player in one campaign playing a Warblade from Tome of Battle. I happen to be one of those people that think the ToB is horribly overpowered (please don't resurrect that debate on this thread! : ) but he was convincing enough for me to let it through. I almost took it away from him recently, but all my players seem convinced his character is not overpowered, and they aren't the type to be dishonest with me like that, so...*shrug* I compromised by taking away the Warblade's ability to 'refresh' Maneuvers during an encounter. He's still playing it, and I'm still trying to decide for myself.
On the other hand, a player in my other campaign loved the flavour of the Complete Divine's Spirit Shaman. Now, *this* class is such a laughably, pathetically weak class that I was tempted to ban it outright simply because it was so horrible it wasn't worth the paper it was printed on. After I got past that initial impulse, I listened to what the player wanted for her character, and drew on abilities from classes in other books to boost the Spirit Shaman to a level I felt was balanced. I again offered the caveat that if it seemed my changes made her *too* powerful, she had to be open to changes later. And in fact, I did end up changing it recently again--by buffing it even further. (Gods, but the Spirit Shaman is a HORRIBLE, HORRIBLE class mechanically. It's got some good flavour, though... : )
The issue isn't whether to allow extra books or not. The issue is whether a GM is willing to invest the time and effort required to run a campaign properly, and what kind of relationship a GM has with his players. Now, if the GM and the players together decide they would all prefer to limit their own choices, then great! Run with it. However, a GM that arbitrarily limits his players' choices because he can't be bothered to take the time to examine what a player wants for his character...should not be a GM, imo.
(Edit: Please note that this response presumes an *experienced* GM. For new GMs, it's a good idea--and in fact, strongly recommended--to limit the game to the Core Three books. I did that myself when I recently tried my hand at running a campaign using Monte Cook's Arcana Evolved, since it was essentially a completely different (if similar) system to 3.5e.)