What time scale are we talking about? If we're asking why oil is more expensive than it was in 1999, I think that's at least partially due to Peak Oil (more due to China and India, though). If we're asking why oil is more expensive than it was in 2009, I'd say it's because of geopolitical instability, speculation, and price inelasticity.
I haven't had a car in roughly three years, so for me, I am thinking in a longer time frame, not a shorter one. Prices will inevitably go up and down some and be influenced by various factors on a day to day basis. But before my divorce forced me out of college, I was an environmental resource management major and went over peak oil in two classes, well before it was some kind of buzz word. One of those classes covered peak oil quite in depth. This is part of why I chose to give up my car when push came to shove for me financially: I believe in the long haul, things will have to change. We will have to walk more, use public transit more, live closer to work, shop closer to home, develop more fuel alternatives and so on. Not everyone will go to the extremes I have gone but the occasional extremist can help make more moderate adaptations look a lot more normal, sane, comfortable, and so on.
(Having given up my car, I do not expect to ever own a car again, having nothing whatsoever to do with peak oil. The short version is that some of the really scary infections that people with my medical condition sometimes get, which doctors don't know how to effectively treat and which 'normal' people don't typically get, are used by environmental scientists for bioremediation of petrochemical spills -- ie they eat petrochemicals. I have come to believe that people like me absorb petrochemicals more than average and that this fact contributes to our seriously negative health outcomes, including picking up infections that think petrochemicals are yummy. I have done much better, health-wise, without a car. Compared to what is supposed to happen to someone with my diagnosis, a little walking is a minor burden.)
Unless you buy everything from local producers who get all their components from local producers, you are indeed affected by oil prices, regardless if you own a car or not.
There are degrees of affectedness, though. I live 2 miles from work, bike in during spring/summer/fall, and my employer provides food on weekdays (technically on weekends as well, if I wanted to go into work then). I tank up on gas about once every 6 weeks, it costs me about $30, and I spend maybe $25-30/week on food. It's well within my budget, and would continue to remain so even if gas went to $10/gallon.
That's a far cry from someone who commutes 20 miles to work in an SUV and spends $60/week just on gas. These people are hurting now. If you have the opportunity to re-arrange your lifestyle so that it's a bit less sensitive to oil prices, it may be a good idea to do so.
I wasn't suggesting otherwise, merely that I am oblivious to what the current price of a gallon of gas is and have been for some time. Since giving up my car, I have been in a gas station twice. I pay zero conscious attention to such things and rarely have the opportunity to just happen to notice it. So, in this longer view, I attribute the general rise in gas prices mostly to peak oil -- which in no way negates the fact that in the shorter run there are many factors which influence the price of any given commodity.
Furthermore, I imagine that even if I did get everything locally grown/made, the price of gas would still have an impact -- unless the farmers were all Amish or something and didn't use gasoline-powered farm equipment.
