Well, speaking as a guy who used to fit the gamer stereotype to a tee, there are some things you can do to improve your social skills and make you more comfortable around the opposite sex.
1) When I came to grad school, I HAD to start teaching lab sections of biology courses. I was petrified at first, but after a few lectures, I steadily felt more confident. When you say something, say it with meaning and confidence- don't pussyfoot around and mumble, stutter, or look down. Look people in the eye and maintain eye contact. I can walk into an auditorium of 500 people now and give a 15 minute presentation without feeling the slightest bit nervous or worried.
2) Feel good about yourself in all apects of your life. In high school and college, I felt awkward in social situations, and was never quite sure how to handle myself. I was also nearly 120 lbs overweight- I was 6'2" and 320 lbs. I felt very self-conscious and was always afraid I would be made fun of (although I never was, I was still deathly afraid of it). Consequently, I avoided every social situation like the black plague, and kept to gaming where I had complete control over my environment.
If that describes you- you have to break out of your rut. Find some social activity you enjoy, and involve yourself in it (for me it was teaching). Also- and I can't stress this enough- get in shape! Yes, its hard. Yes, its tough to stop yourself from eating the foods you adore to the point where you are stuffed. But it is worth it, both for your self-esteem and long term health. Three years ago I started walking 3 miles a day, cutting out the saturated fats and simple sugars from my diet. Two years ago, I started going to the gym 3-4 times a week and doing some fairly intensive weightlifting. Now, I'm 6'2" and 240 lbs, very healthy, and a physique much more like Triple H than Louie Anderson.
I feel a lot better about myself, and others pick up on that, and are more likely to react positively to me than before.
3) My doctoral advisor gave me this advice for dealing with women- and it works wonders. NEVER look down or away when you talk to women you are interested in. Look them in the eye (not the chest) and listen to what they say. Carry on a conversation with them, and make comments based on what they are talking about (basically, treat them like any person deserves to be treated). Yes, they are girls- but surprisingly enough, they often have something valid and interesting to say!
Seriously, you have no idea how many stereotypical "gamers" I have seen stammer, sweat, and act like complete pigs around women. Women do like a confident guy, and looking away, fidgeting, or acting distracted is a sure sign of a guy with low confidence. The other thing is to tease them nicely- nothing mean, but just playful jokes or jibes. The best he could explain this to me was that it sends the message that you are so comfortable around her and about yourself that you can even take the risk of offending her- but many women seem to see this as a sign of condifence and will respond VERY positively. God, if someone had told me I would be giving dating advice to anyone 3 years ago, I would have thought they were nuts. I never dated in high school or college, and didn't have a serious girlfriend until 2 years ago! Now, I can go up to very attractive women, and 80% of the time within 10 minutes have her email address or phone # (and yes, it drives some of my buddies nuts since I am NOT the player type). And you know what? When I tell them I game, or make a geeky reference- they don't care. In fact, many VERY attractive young ladies who have been former students or just acquaintances have seemed really interested in gaming once I explained it- so its not that they avoid geeks, women avoid geeks who are not CONFIDENT. However, don't be an ass- nobody likes a horse's patoot.
You're right to some degree fusangite- fear is a neurobiochemical response (and I should know, I am a neuroscientist). But you can alter the contingencies under which you feel fear, and thereby control under which circumstances you are anxious. Start small- just try a few things that make you anxious and be open to what happens. Remember, who cares if you do embarass yourself? Most people won't remember what happend past a few hours- so the only one who is punishing you is you! Have a sense of humor about yourself and life in general- if everything is life and death to you- you're always going to be stressed out and unhappy. Know when to laugh at yourself and move on- don't dwell on it. I know I have made a fool of myself in my lectures several times, but rather than get flustered, I make a joke about it and move on. You'd be surprised how forgiving people will be if you approach life in such a way.