Sheldon Cooper: Sheldon has Asperger's Syndrome. Wikipedia says that the show's creators try to deny this detail, but think about it... Sheldon often only thinks about himself, and he never takes himself as a rude, condescending character; he just assumes that all people are capable of reaching the same conclusions as himself. Sheldon lacks social skills to the extreme, yet is a well-versed dancer. Despite being raised by a deeply religious mother, Sheldon rejects all religious indoctrination, as it is not consistent with his model of how the universe works.
Leonard Hofstadter: Leonard is the most realistic character on this show. He has lapses in social judgment, but he usually is aware of his own situations, ethics, social customs. His nerdiness certainly defines important aspects of his character, but he is capable of knowing when to bring up nerdy topics and when not to... usually. Leonard reminds me of my college adviser, Dr. Lemley. Lemley wrote a physics test on Klingon ships moving in outer space at the speed of light; this is a clear indicator of the nerdy side to himself. He also gets along with people, has some odd characteristics, and has a healthy, happy family.
Howard and Rajj: I am lumping both of these characters together because I observe their struggles with women. Most people perceive physicists to struggle with women, and most people are right. I think the reason that this is often the case is that physicists think on a purely logical basis... all the time. We are programmed to think this way, and when we see ourselves talking to a beautiful woman who, like most people, knows little to nothing about physics, we don't know what to say. We do know that talking about work won't interest her, and if we are nerdy outside of work, what is there to talk about? Star Wars? Settlers of Catan? Most people in general aren't interested in Settlers or Physics, so it's no surprise that it is difficult to impress a woman with such knowledge.
Penny. Penny is not a dumb blonde. She looks dumb because she stands near guys who know way more than most people in general. She works as a waitress, struggles to make a living, and finds herself chatting up Leonard and Sheldon just to pass the time. She often mediates between the audience and the characters by showing how it is unreasonable to expect ordinary people to understand Newton's laws and uncertainty principle. I think it's kind of sad that we don't value mechanical understanding of our world a bit more.
I had a college professor who is not like any of the above. Dr. Velasquez is a character with very good social skills; he is an international competitor of ballroom dancing and an nth degree blackbelt in three different martial arts. Of course, he also has a PhD in (I think it is solid state) physics. He is a great public speaker and earns much respect from the community...
The thing that interests me are the stereotypes about science people. I have a Dilbert comic posted outside my classroom where Dilbert attends a scientist anti-defamation league meeting where they want to dispel the myth that scientists have no social lives. Nevertheless, they agree on Saturday night for their next meeting. Why are so many scientists characterized by a lack of social interaction? Every field of study requires people to interact with each other, and science is no exception. Personally, I used to shy away from many social situations because I was interested in things that I knew would bore most people. Sometimes I'd talk about them anyway, just to show off how smart we scientists are. Since then, I have developed some interests of "normal people," such as sports, video games, and videos of funny kittens on youtube.
I think I have explained the mechanism that feeds the stereotype. I also think that a truly educated person can talk about anything. Einstein had pretty good people skills; he was also a gifted musician, an artist, a literary scholar, and a social activist. He once turned down an offer to become Israel's Prime Minister. Dr. Velasquez is another example of a jack of all trades, as explained before.
I strive to be the same same thing in my own life. I have my strong set of political views. I appreciate some works of literature; I play tennis, I used to play billiards, I was a stand-up comedian in college, and a pretty good one at that. I once won a tournament of guitar hero, having only just started the game 2 weeks prior. The person I beat had been playing for more than a year. I have since dropped the game, for the real instrument. I think the best thing a person can do in life is enrich themselves in as many things as possible. Albert Pujols is a multi-millionaire who once his baseball career ends, despite his large financial success, he will not likely experience the pleasure of intellectual success, and success across several different subject areas. My advice to my students is to enrich themselves and develop multiple passions. You never know which one turns into the career. Even then, the average human will change careers over 3 times in a life. This means that you will probably change your major in college at least once, if not several times. Many students of mine could major in anything they want. This ability may seem like an ill-gotten gain, but in the future, it opens up so many possibilities. Don't develop the attitude that any content area won't be useful in life, because the skills you gain in that class may be very important in the future.