What happens in a corporate environment if a supervisor offers a raise or promotion to an employee, and the employee turns it down? For example, if the employee said that he doesn't think he deserves a raise/promotion, and wants to remain at his current level and salary.

Generally nothing, but it will look bad on the employee's record and they may not be considered again.

It is frowned on to NOT take more responsibility, especially if commensurate pay is offered. Now, if there is a particular reason to not take the extra work, like a family situation (sick child say, needing time/attention), and that is explained, then it's likely not a big deal, but otherwise, Scott is correct - not taking the job without a good reason would likely be shooting yourself in the foot career-wise.

What if the employee accepts the promotion, but tells his boss he wants to remain at the same pay with no raise?

Then the employer is likely to question his mental heatlh. Its more understandable to not want more responsibility, but more pay?

Yes if he turns down a raise he will be very suspect at least in the US.

A person may turn down a promotion, but then they will most likely never be asked again.

Most raises are more based on cost of iving issues, and pay rates for a position to keep your pay in line with those working under you.

I don't quite understand why one would turn down an offer of a raise. Take it! If you are in a non-profit and feel you shouldn't take more money, you can always return it to the organization in the form of targeted donations to the programs that you support. I have done this at non-profits where I worked... donated back to my employer organization but was glad to control where the money went as the donor.

As for responsibility, most organizations are growth-minded and if they are well run, they want to see their employees grow as well. If it's a matter that the new title would greatly change your life in ways you don't want to (new job requires travel, working weekends or things like that) or if you don't like the job description as well as what you're doing I would recommend you be very clear and just say, "Bob, I'm so delighted with this offer of promotion but I have to tell you, thinking it over and discussing it with my spouse, you know, I don't think I'm up for the travel. It's a great opportunity, but I'm so happy with what I'm doing, would you mind terribly if I decline the promotion and stay where I'm at for the time being?" But you may be viewed as lacking motivation, and as others have said, you may not get another chance.