A psychology textbook entitled General Psychology by Weeks and James attempted to define eccentricity. These guys did a pretty good job. Essentially, they said that eccentrics may "act" like crazy people, but the difference is that people with mental disorders "suffer" from them, while eccentrics know they are different and are pleased with that fact. Eccentric people's thought processes are not usually illogical but are simply unusual and/or abnormal, and strangely enough, when tested, eccentric people have a lower incidence of mental disorders than the general population. This insinuates that the eccentrics' unusual behavior and failure to comply with society standards may even be beneficial to mental health. David Weeks came up with this list of fifteen characteristics of eccentrics. The first five are present in almost all eccentrics, while below that they are less able to be generalized to the eccentric population. Having ten or more of these characteristics may signify eccentricity.

(Weeks & James, 1995)

I'd just like to note that "Bad speller" is one characteristic that I don't think should be on this list, since many of the people I know that would be considered eccentric are also spelling nuts.