If you're going to school fully online than the answer is obvious, but it's not always so easy to tell with brick-and-mortar colleges. The good news is that many traditional college students manage college life just fine without having a vehicle (and avoid all those annoying parking tickets given all too often to the students who do have vehicles). By not having a car in college, many frugal students save money they would have otherwise spent on gas, maintenance, insurance and car payments.
First of all, look into the city that you're relocating to. How expansive and accessible is its public transportation system? Are there city bus routes to the locations you'll be visiting most often? Think grocery stores and downtown destinations. Is there a subway if you're planning to live off campus?
When visiting your college's campus or merely exploring a map of the campus online, evaluate how close together the buildings are. Think about the distance between the residence halls (or your apartment) and the main facilities. Is everything easily accessible by foot or by bike? Many of today's universities, particularly those found in major metropolitan areas, have to spread their facilities apart by fairly vast distances, so you will need to evaluate whether those distances will be manageable or not. To make up for these distances, many universities offer students a free campus-based bus transit system to get them from point A to point B. You will just need to ask yourself if you want to make yourself fully dependent on that system (after all, campus bus routes can be cancelled on short notice) or if you prefer to have a vehicle as a back-up plan.
Another thing to consider is whether or not you will be working in college. Unless you stumble upon some fantastic carpool plan, chances are you will need a reliable vehicle to get you to and from your part-time or full-time job. If you plan to get a job somewhere else besides on-campus or in walking distance from your campus, plan on having a car.
Speaking of carpooling, if you plan to go without a car in college, you may want to get comfortable with it. Carpooling may be your only way of getting home for holidays or breaks if you don't have cash for a cab or airfare. So choose your friends wisely—particularly ones who have wheels!