You also have to be careful about what you mean about a great professor as well. There has been an ongoing battle within schools, because universities are often caught up in the prestige game, which is based on the research the professors do and get published, and to be quite blunt the superstar researchers may not be great teachers but have a reputation for what they published. I had a guy teaching a class who was in serious consideration for the field medal in math years ago, and quite honestly, he couldn’t teach his way out of a paper bag and made pretty clear he resented teaching us peons (on the other hand, I had a chem professor who had done some amazing things, all kinds of first rate research, patents, you name it, who was hyped up to teach, and this was a first year chem for majors class, loved that guy).
Besides things like lab lectures, recitations and lab courses, or recitations and help with math, the only other classes I routinely saw taught by grad students were things like the required expository writing (that we called suppository writing), some of the lower level math classes (calc1 and calc 2), and they were generally Phd students already with a lot under their belt, also had it in some of the classes that were core classes, like a class in Japanese literature I took, it all depended. TA’s are not necessarily inferior teachers, I had some who were first rate teachers.
adjuncts, too, are not necessarily bad, depending on the course, a lot of times adjuncts are people who have worked in industry, they often are master’s level at least degree people, and in certain areas that can be really, really valuable (in grad school, the guy who taught my TQM classes was adjunct, he had been the head of NYNEX office of quality, and man could he offer practical advice on how to deal with tough situations), so they might be better than that ‘great teacher’ who thinks teaching classes is an annoyance , keeping them from their research. Sadly, a lot of schools have been hiring ‘wandering gypsies’ to save money, adjunct and assistant professors, who teach at many places and to be honest, even if they are good teachers, get burned out from what I hear, so if you see a program, especially undergrad, where a lot of the teaching is adjuncts or assistant (non tenure track) teachers, you may want to question that.