It really depends on the program. In places like law and medical school, I believe GPA is at least fairly important in terms of class ranking and what not.
In other disciplines, and especially when going for a Ph.D., it's much less crucial. I know in my doctoral program--and this is generally the same for clinical psych programs around the country--anything below a B is considered failing. You're allowed one C, after which you're removed from the university. The grades themselves, beyond that, aren't very important, even when it comes to placement for internships. What's more important is the material of the course, and being able to use that material in an applied sense. Beyond that, as others have mentioned, there is also great importance placed on your research projects and clinical practicum experiences.
Edit: I should mention that if you're going for your Master's with the hopes of transferring into a doctoral program afterwards, then grades become a bit more important. Basically, you want to show that you can earn as close to a 4.0 as possible, after which you should be alright.