I know this topic has already become old, but I thought I'd atleast give my thoughts on the subject: bullying in Eve Online.
There has been a recent uproar following The Mittani's actions at Fanfest. The way I see it the responses can be classified in three groups: those that feel his actions where outrageous and CCP was way too light on him with the month ban, those that feel CCP can stuff their ban, because it turned him into a martyr, enhancing his credit as the "villain" in Eve, and finally those that don't really care about the politics of a science fiction game and just try to enjoy it regardless. I believe I happen to fall in the latter.
When I was in preschool my teacher taught me a simple technique to bullies:
"Just ignore them, they want the attention."
True enough that this advice did little when my head was being stuffed into a toilet (don't worry I'm not going into a therapy session here, just bear with me). I have, however, found the advice useful in online gaming. From the trolls in roleplayers to the douches in first person shooters.
So far, in my short stint in Eve, I have come across all kinds of people, but generally I find that most people act reasonably. Every 1v1 request has been honored so far, even with accompanying gl's and gf's, and the few smacktalkers in local I just ignore.
Although I will agree that you should not be completely ignorant. Eve online has one of the most complicated political system in any game I have ever played, and just as in real life, you should atleast keep an eye on the happenings so that you cannot say "but, I didn't know it was Hulkageddon!!" CCP was even kind enough to add a warning for the Burn Jita event in the log in screen (see above). Just a reminder, your playing a game where trust is a precious commodity- spend it wisely.