It’s the first time I’ve gotten this term used to get to my blog, but it’s one that is very, very important. As far as I know, all schools have a qualifying exam of some sort. Some have it in one sweep, others have it in “waves”, so there’s a part 1 which might involve answering questions (written) or presenting a topic and “defending” it in front of an examinating committee, and part 2 can be more focused, although it really depends on the school and which order they do things (they might invert things from what I stated before). If in doubt, always check the department’s website which will more than likely have a list of steps each grad student must complete before being able to work solely on the thesis without any further exams.
My school only had one. You can read more about it here. My BF’s school (where I’m currently a postdoc) has 2 for his discipline, a general one, and a comprehensive one. His department is not the same as mine, nor are our disciplines of study (duh!). In my new department the qual is taken no later than your second year and it’s only one part, related to your field of study (or based upon your proposed thesis research).