Well, to be honest the stereotype is there for a reason. I think maybe you've been spoiled by ENWorld and your current group- I know I have. ENWorld tends to have the higher-functioning gamers posting here- the ones NOT living in momma's basement, with a job, education, social life, and who don't blatantly display mental illness. My group consists mostly of friends I met in high school or college. We have an aeronautical engineer, computer systems specialist, divisional manager of a credit card company, ad exec for Bass Pro, social worker (ad exec's wife), media coordinator for a local TV station, psychology grad student (my sister), and professor of neuroscience (me). None of us have ever been diagnosed with mental illnesses, we all have professional jobs, social lives, friends outside gaming, and relationships that are much better than the average American's (meaning no cheating drama, screaming fights, etc). Yes, we all tend to act goofy and make nerdy references when we get together, but we aren't ashamed of being geeks- we're comfortable with who we are, and don't care what others think of us.
A few years ago a couple in our group moved to Phoenix AZ, and we were looking for one or two new gamers. On a whim, I put an ad in at a local game store, after being advised by the owner "careful what you wish for". Wow, what an eye-opener. I've been spoiled by my friends and gaming group- we ran into a LOT of real nut-jobs, mentally unstable people, and many were of the unwashed gamer geek stereotype. I'd say for every 20 people we talked to, only ONE was someone I'd associate with, and we did finally pick up one guy whose schedule and gaming preferences matched ours. He was overjoyed to be with us, saying he'd moved to the area a few years ago (he's the media coordinator), and was shocked at how hard it was to find "normal" gamers who wheren't psycho, obsess on gaming 24/7, and who didn't have mental ilness and/or severe social problems.
Gamers who tend to get noticed by the public are the ones who are the stereotypical unwashed, horrible hygeine, neckbeard, quasi-goths who have horrible social skills and stick out like a sore thumb in normal society. Many people in my group keep their gaming quiet at work- only me and the computer systems specialist freely admit and talk about gaming to non-gamers. Most people react with surprise when they find out we game because we don't fit the preconceived stereotype, and several students at my university have asked to join my group or form a new one. And far from being ridiculed for gaming, I've found people open up to the idea of gaming once they knew a few "normal" gamers- not to mention that a lot of the young women in college are open to the idea of gaming as long as the guy doesn't give them the "creepy" vibe. (And no, I don't fraternize with students- both due to my university's policy and ethical reasons).
As for why gaming draws so many of the unwashed geek stereotype- I don't know, and thats probably a discussion better left to another thread. I have a strong suspicion that a lot of the "normal geeks" out there do what we do- band together in tight groups and don't tend to float around a lot to different gaming groups with the exception of the occasional convention, while the unwashed geeks tend to creep people out, never get accepted into a stable group, and hang out in gaming stores grousing and freaking out walk-in customers and women who go in. If thats who the Average Joe thinks of when he thinks gamer, then its no wonder we have a negative public image.