Do Accounting majors have to take calculus?

It depends on the university, of course. 

In my experience (YMMV), accounting majors are typically required to take business calculus for two semesters. Engineering and natural science science majors, typically have three semesters of introductory calculus. The business calculus didn't get into multivariable and vector calculus. 

I'd say the accounting field might be saturated, but it's not *over*-saturated.  Accounting is one of the more recession-proof majors out there for new graduates. 

Nothing guarantees a job, of course, and you'll still have to work hard and get good grades. But with a decent GPA and couple of good internships under your belt, you should have no trouble finding an entry-level position in accounting; you can't say that for any other bachelor's degree, except maybe engineering. Even nursing is becoming over-saturated. Your opportunities will expand with a CPA certificate. 

Calculus is the study of rates of change of functions and is one of the most common mathematics courses offered by a mathematics department. ... Most accounting programs do not require students to take calculus, but some do want to see that students in their program have previous experience with calculus 1.

thought you did calculus in high school ...

I am not an accounting major, in fact my degree was in international relations. Even I had to take calculus.  In fact, I took Calculus 1-3. Calculus is one of those classes just about everyone takes even if they never use it again (I am not a research methodologist and data analyst and I have not used calculus since college). 

Yes, you'll likely have to take business calculus. And accounting is absolutely oversaturated and competitive.

The general answer is yes; all business administration majors (of which accounting is a concentration) are required to take some form of calculus.  Many colleges, however, have different types of calculus courses.  Accounting majors usually have to take something many schools refer to as business calculus (at my college, it was referred to as Quantitative Analysis).  The course is weighted more towards business style problems, such as break even points, present and future values, and the like.  The skills taught in the course are very important for business leaders to know.  

Accounting is a hard field to break into.  That was true even when I broke into the profession (thanks to racquetball, actually) back in the 1980s.  Almost all employers want experience, even for entry level positions.  Once one gets 2 years experience, though, his demand in the job market rises rapidly.  

I imagine it varies by program.  Accounting majors at my university are not required to take calculus.  

As for the job market, there are a number of things you can do with an accounting degree - some of those areas of work are pretty saturated while others are not.

Calculus  seems to be some sort of GOD course, forced on nearly everyone regardless of the need for future use.