So, I imagine there are SEAS core classes CC students can’t get into but other than that? The grad schools? The law school? The med school? The business school? Are there classes in the College that are only open to majors? Classes that you have to apply to get into? Are there certain classes that are in such high demand that you probably won’t ever get them in your four years? If so, do you choose backups in course selection, can you audit any course, what are your other options?
I would appreciate any insight even if you can’t answer all the questions! Thank you!
You cannot take classes in the law school, it seems: http://www.law.columbia.edu/registration/cross-registration
"Law School courses are open only to students enrolled as FULL-TIME Columbia University graduate degree candidates. Full-time graduate degree candidates may take up to 2 (two) Law courses per term but not more than 4 (four) Law courses during their entire Columbia course of study. JD and LLM foundation courses, legal writing, research, clinical, and externship offerings are NOT open to non-Law students.
REGISTRATION AS AN AUDITOR IS NOT PERMITTED FOR ANY LAW COURSE and INFORMAL AUDITING FOR MORE THAN ONE OR TWO CLASS SESSIONS IS NOT ALLOWED."
Though if taking classes at an Ivy League law school is one of your goals as an undergrad, you can certainly do it at Penn: https://www.law.upenn.edu/registrar/for-current-university-students.php
"Penn Law welcomes students enrolled in professional and graduate programs at Penn, and upper-class undergraduates, to take a class at the Law School. Penn faculty and staff are welcome to take the Master in Law courses (ML).
We appreciate the voices of those with varied backgrounds in the law school classroom. Whether you are interested in exploring the future possibility of law school or in complementing your career or studies in another discipline, we are certain you will find Penn Law courses and programs of study that interest you and meet your needs."
I took classes in the law school while an undergrad at Penn and I didn’t have to request access for one of them since it was a course that was actually cross-listed with the history department in the College. It’s important to consider these differing institutional orientations towards your academic goals! 
I doubt is any medical school will let undergraduate students take classes there.
@PennCAS2014 @TomSrOfBoston Thank you for your responses!
Undergrad registration between CC and SEAS seems totally open. The classes that are restricted to majors really would just be ones with lots of pre reqs but if you took the pre reqs you’d be fine. There are lots of major/double major/minors that span both CC and SEAS so it’s not uncommon to find non-majors taking upper level classes in other depts/schools. There are a few classes that are in high demand due to content and/or teacher but it’s not a huge issue more that it’s fun to try and get some of these. The way registration and shopping period are done it’s easy to register and/or wait list for more classes than you need and then figure out over the 2 weeks what to keep and what to drop. Great way to figure out best level for some classes where you aren’t sure and testing/pre-reqs don’t apply.
@ccccguideg Thanks this was exactly the kind of answer I was hoping for