Nodding along with the above three posts. I am an introvert. While I do really enjoy sitting down with a small group of people -- maybe 1 to 4 others -- and having a good chat or whatever, I wouldn't want to do it all the time, and I definitely need time alone. (Which is why I sacrifice sleep to be up by myself when everyone else is snoozing -- the cat is welcome to join me, though.)
I remember in school wanting to reach out and talk to others, but rarely because I wanted more friends (it was never difficult to reach out and talk to those who became my good friends). Only because I felt like there was something wrong with me if I didn't have as many friends as everyone else (or, really, as the popular crowd), or if I spent a lunch hour by myself reading. My bus ride all through elementary and high school was about an hour each way. Even though I was never too far from the school, I lived in a rural area and was one of the first to be picked up in the morning/last off the bus in the evening. It was great -- so much time to myself. My mom has told the story that when I was young, I told her that I was glad when my seatmate got off the bus. She was worried that there might be some bullying or something going on, and asked why, but I told her because then, it's just me and my imagination.

It is so freeing to realize now that I don't have to be constantly chatting/socially engaged with someone to be normal. But, long story short -- some people aren't (and don't want to be) extroverts, and that's OK.
I do think, though, that there is a difference between introvert/extrovert and shy/outgoing. Introverts thrive on/recharge their batteries on alone time; extroverts thrive on time with others. I think you can have shy extroverts and outgoing introverts.