The local bus is free for college students, which is really nice. It has its flaws, though. It is known for not being very reliable, but it's not like you should expect to miss the bus every day. It also runs very infrequently on weekends. You can also sign up to be a Zipcar University member, which means you can rent a Zipcar even if you're under 21 (as long as you are a student). This costs money, but it's surprisingly cheap unless you want to go very far away. I use them for dental appointments and nearby concerts, but some people can afford to use them for all of their errands or for trips to big cities like Boston. Don't bother with the local cabs; they're WAY too expensive.
If you want to go to a big city, you can use Peter Pan or Megabus. Peter Pan is godawful but it's the only way I know how to get to Boston. It's expensive and always late. Megabus is pretty good and can get you to New York City; the prices are reasonable, and if you buy your ticket early it's dirt cheap. You have to take the public bus to the mall first, but that's free. Unfortunately, it runs at somewhat inconvenient times on some days.