I'd like to suggest renaming the fanatic badge to something with a more positive connotation. I'm taking regular days off SO just to avoid it (which is hard, as I have to be careful about what Google hits I click). As I know badges are there to support a certain behavior (visiting SO in this case), I feel that at least for me, the naming of that badge has the opposite effect.
I guess this just goes to show that you can't please all of the people all of the time.
For me, 'fanatic' seems a perfectly accurate description of anyone who is present on 100 consecutive days on any of the StackOverflow sites (and yes, I have a Fanatic badge for StackOverflow; and yes, I'm proud of it; and no, I don't want it renamed; and yes I was livid when my vacation in obscure corners of darkest England meant that my sequence was broken at somewhere around day 90 and I had to start over).
Wow. There's people here who actually cried on the 98th or 99th day if they missed logging in for this badge... I got mine on meta on 2010-01 (New Year's Eve still in my timezone) and thought it was a great present.
Still, you're right, the definitions of "fanatic" are largely negative. How about "Connoisseur" as a replacement? It invokes the image of a person who is sophisticated and distinguished, rather than someone who might be a raving lunatic.
It should just be shortened to "Fan" maybe? While Fan is just short for Fanatic, nowadays the words have two different meanings, with the former being associated with Supporters of Sports Teams and the latter being associated with Supporters of Explosives.
We already have a Supporter Badge, so that name is taken. Groupie would be another name for Die-Hard-Fans I guess, but it's not entirely positive either.
Websters: marked by excessive enthusiasm and often intense uncritical devotion
MacMillan: someone who has very strong religious or political beliefs that often make them behave in an unreasonable way
Collins: a person whose enthusiasm or zeal for something is extreme or beyond normal limits
AHD: A person marked or motivated by an extreme, unreasoning enthusiasm, as for a cause.
Times change. So does the language.
This proposal is in BAD need of revival!
To add a suggestion for an alternative name independently of the general suggestion of renaming the badge, I'd like to suggest
hard-working here (both in the sense of working hard at SO and not always working hard at work, as discussed in Podcast #82).