gaga_megan

I think it depends heavily on the program. At my master's institution, there was a comprehensive exam covering the first year material. There were three levels of pass/fail: PhD pass, master's pass, and fail. You were required to get a PhD pass in order to continue onto the PhD classes.
At my PhD institution, there is only a master's exam for those wishing to get a master's degree. PhD students are not required to take the exam, and there are only two levels of pass (pass or fail). 

Most programs have two written qualifying exams, a first year exam and an advanced exam. The first year exam generally tests you over basic applied and theoretical principles covered in your first year (e.g. for theory, most of Casella and Berger). An advanced written exam would generally be after you've finished your coursework and taken in your third year, testing you over advanced concepts in your upper level grad classes. 

Almost all programs have a written exam covering Masters level statistics theory (at the level of Casella and Berger) and possibly applied statistics. If you do not get a PhD-level pas on this exam within two or three attempts, usually you'll be asked to finish with a Masters but not continue on in the PhD program (at this point, some students will also, on their own volition, elect not to continue on to the PhD). At some schools, those who DO continue on the PhD track have to then take a second written exam (or exams) based on the PhD-level theory classes.  At some schools, there are tests in different subject areas (e.g. advanced statistical theory, probability theory, applied statistics, or whatever) and you pick two of the three and need to pass those. 
This was how it was for the PhD in Statistics at both the department where I got my Masters and my current department (i.e. two sets of exams: a "Basic" exam and an "Advanced" exam). The "Basic" exam is (in theory) meant to undo any admissions mistakes, but is obviously also subjective.