So on my second day of biking in Chicago, I was doored for the first (and hopefully last) time. It wasn't that bad in my case... I saw the door opening, yelled "Hey!", and both braked and swerved out of the way. The driver was very apologetic, and I told him not to worry too much as at least nothing bad happened, but that he should be more careful. Recovering from his shock and embarrassment he said, "Man! I thought that stuff only happened in the movies!" I found his comment funny, but the whole situation could have been very tragic; I got away with nothing but a few bruises on the knuckles (which bounced against the edge of the door), but there was a bus about ten feet behind me. If it were closer when I swerved, things could have been much worse.
But perhaps this situation is all for the best as it has served as somewhat of a wake up call. Since then I've done a lot of research both on how to avoid being doored and on bike safety in general, with a lot of help from some bike-savvy friends. I now know that you should always keep yourself at least three feet away from all car doors to avoid being hit (four is better, five is ideal). I've also found a nice essay on the subject (including some examples of people who have died or been seriously injured by being doored) as well as advice from the City of Chicago. These are good reads, but nothing compares to Bicycle Safe: How to Not Get Hit by Cars. Seriously, it's a must read for any urban biker.
Anyway, I'm glad that I'm biking a bit better informed. But I'm definitely going to keep my alertness level at its highest and stick to neighborhood roads. My sister just told me about how she was a passenger in a car when the driver parked and doored a bicyclist, knocking out the guy's full set of teeth. To be honest, I don't take the best care of my teeth, but I sure would hate to lose them all at once.