Game Master advice is full to the brim of one bit of wisdom. Seriously, everywhere you look you'll find it there. Odds are you've read it countless times, and I know I've referenced it here at least a half dozen times. What is that piece of advice? Well, it's simple. "Never say no to a character." It can be expanded on, usually with the following "Say 'yes, and...', 'yes, if...', 'yes, but....', but always say 'yes'"
Now, this is good advice for GMs, and especially for new GMs. The idea is that you should never be telling a character that they can't do something, just that they'll have to earn it some how. They'll have to roll really high, get really lucky, work very hard, etc, etc. To the player, you can say no, but not to the character (that is its own ball of yarn though). This advice is good advice because it helps prevent rail roading, and helps you - over time - get better at thinking on your feet and handling what your PCs throw at you.
However, every rule has exceptions. I believe that firmly enough that it is one of the few cases where I will use an absolute. However, in mulling it over I can't think of any situations, even very specific situations, where I would say the right course of action is to say "no" to a character. I can think of tons of ones where I might say no, especially if I was tired or in a mood, but not where I could objectively tell someone that they should say no.
How about you? Are there times - however specific - when you think it is ok to break this bit of advice? Have there been situations where you've flat out said no to someone, and would do it again now that you look back on it with hindisght? Or even situations where you didn't say no, but now think you probably should have (again, looking at it objectively)?