| Hi zzangkwonyg,
The vast, VAST majority of Harvard courses are open registration, where they would never turn down a student because of size constraints. Some courses, like Ec 10, have up to a thousand students.
However, there are exceptions, primarily in composition workshops (Introduction to Screenwriting, Poetry Writing, Fiction Writing, etc.) and a few special English courses (The American Transcendentalist, The Poetry of Emily Dickinson, for example). These courses are limited to 15 students, which makes sense because they want an intimate workshop environment.
There are also Freshman Seminars, which are special courses taken Pass/Fail in freshman year that are in a very close environment with a professor. Those are all limited to 15 students (but they're naturally special).
So, generally, the courses are either completely open, or they're special very small seminars. Almost all the seminars are primarily taken as electives (and would never be a concentration requirement, though some would satisfy English or History), so generally you would never expect the size limitations to ever get in your way for classes that are important to your concentration- no matter how many hundreds of students are taking Introduction to Statistics, or whatever, they'll still let everyone in.
One other case that bothered me last year is that Literature and Arts B-11, The Art of Film, is limited to 200 students, for the simple reason that the theater they use has only 200 seats. There's a lottery for positions in the class (which I unfortunately lost last fall).
I hope I answered your question. | 
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