Should I take my car with me to the University of Missouri?

I agree with Kyle, I don't think I've ever seen a college where students regularly drive to classes unless they live off campus, but then they typically just park once and walk. Often a parking permit is only good for one particular lot, and freshmen usually get the lots in the worst locations (way off on the far edge of campus), if they can even get a permit. Lots that are actually close to academic buildings are usually reserved for faculty.

If you're living in the dorms on a meal plan (you don't need to go grocery shopping every week), and you don't have an off-campus job, then you probably don't need a car. The college probably has shuttles, and students usually get free/discounted public transit passes for city buses.

Pay the campus a visit and decide for yourself. You can check out the lay of the land, so to speak. Also, that way you won't be blindsided when you actually need to arrive on campus for classes.