Trying to keep this short and useful:
Living car-free in a city is much different than the suburbs. Without public transport, it's either riding your bike, bumming a ride, or borrowing a car (parents'?). It can be tough, but not impossible. Living in a city, I don't see any reason one can't easily live without a car, providing a moderate amount of planning in advance (home location with respect to work/school)
Here are my thoughts:
1) when in social situations, you can generally ride with a friend. I used to be the one with a car, and I often drove around friends of mine without cars. And these were kids without bikes.
2) - depending on the situation, borrowing the parents' car is probably useful for those "special circumstances" (dates, going to the hardware store, traveling distances)
3) - Tandems. Dates. I think they were made for each other, provided the weather is pleasant. If not, see #2, or get a girl who bikes. I don't think I could see myself with someone who refuses to bike, but that's just me. Spending $500 on a used tandem bike is like two months of car insurance. But you can keep it forever.
4) - When you head to school, it should be simple to live on-campus without a car. A lot of schools don't let you have one. If school is a long way from home and you want to visit for the holiday or a weekend, see if there's anyone else who's going the same way at that time. At my school, we had a "ride board" where people posted if they were driving somewhere or looking for a ride. It works out for everyone, because gas money can be split.
5) - Consider "carsharing" services. I'm not sure what cities they're in. I've only lived in two cities myself: Boston, MA and Sydney, Australia. Both had car-sharing companies that basically let you borrow a car/van for a couple of hours for an hourly rate. It fits perfectly with a cycling lifestyle. (Google "GoGet carshare" or "zipcar")
If i could redo my younger years, I would not have bought a car at 16. I would have borrowed dad's minivan (like I did when my car inevitably broke down) when I needed it, and biked. I would have stayed healthier, and had a lot more money to spend on things more fun than gas and insurance and repair parts....
Okay, I'm done.