Common for department guidelines/traditions to require tenure track academics rotate courses? In the context of academics in research universities on their tenure track; how common is it for their promotion and tenure to be conditioned upon how many courses they have taught? 

Is it more or less likely that they are given an initial set of courses to teach and that this remains as the class set continuously? Would it be normal to find that a department explicitly requires academics to rotate courses throughout their tenure track experience?
Almost all top research universities also have a teaching mission. Most have an undergraduate teaching mission as well. Some of those have a special faculty track for the lower level courses (Professor of the Practice, say, at Duke), but many also require senior faculty to teach a few courses per year. For some courses it is common for certain faculty to specialize, say the Compiler Course in CS, for example. But, in the absence of specialized track faculty, everyone has to have some contact with undergraduates, even if it is as a coordinator of all the TAs teaching, say, Calculus I. 

Eventually junior faculty need to be integrated into this system. Given that the tenure probation period is typically about seven years, only the earliest part of this is likely to be free of teaching responsibilities. But for a new faculty member, it is common enough to get a year without teaching duties and another year or so of teaching easier courses for which a lot of resources already exist. Of course, you can probably request a specialized course as well. 

But, in many and I hope most places, the teaching assignments are more or less decided by request and consent rather than being imposed, as long as every course has coverage. An especially collegial place will likely give new faculty first choice (or second,...) of courses, rather than dumping the hard ones on the new faculty after the "plums" are chosen by the senior faculty. 

And, of course, in some fields, having extensive external funding can relieve you of the need to teach at all. 

But a new faculty member teaching an intro level course will find a bit of shock when they find out there are 500 students in the course and you need to manage 20 or so TAs as well as give lectures. 

As to the question of tenure, some places don't care too much about whether you can teach undergraduates effectively provided that you are a superb researcher and can effectively teach grad students and, especially, direct doctoral work. Others will place more emphasis on teaching. Most will also place at least some emphasis on flexibility. How willing are you to "take one for the team" and teach a difficult course? Everyone needs to do this occasionally, of course, and refusing shows lack of collegiality that can lead to problems at tenure time. 

But, also, I hope and expect, that most research universities will find ways to "nurture" tenure track faculty and integrate them into the local culture as well as supporting their research goals.