The majority of Yalies find that they simply don't need a car on campus. Most places in New Haven are within walking distance or a brief shuttle ride away (there is a real-time shuttle tracking system online!). Most social activities are contained on campus so you don't need to drive anywhere to have a great time. Plus, New York City and Boston are a mere train ride away.
When you really need a car, Yale offers a great program called Zipcar that allows students to rent a car by the hour or day for a reasonable cost. There are 11 Zipcar locations on the Yale campus, so it is easy and inexpensive to get off campus when you need to.
Some students who live nearby may want a car to get to and from home quickly. However, a car can be more pain than it is worth. Most students observe that the parking lot locations are inconvenient and that the costs are unreasonable (New Haven is a city). In the end, it might be cheaper and easier to use public transportation and rent a Zipcar for one-time needs.