I know I'm an introvert because of many reasons:
My tolerance for stimulation is low. When I'm in a small room full of people who are talking very loudly and over each other I start to feel like my brain is going to explode; a borderline panic-attack I suppose. The same goes for listening to music (that isn't my preferred music) at insanely loud volumes.
Also, I noticed that about 90% of my video games are one-player games; mostly RPGs. After a long week of classes and work, nothing sounds better than spending most of my weekend in my room by myself surfing the net, watching a movie, playing some video games, reading a book, etc. The last thing I want to do is go out and "have fun". I know it sounds lame and boring, but it's just how I am.
Unless it's a psychology (my major) class, I usually never raise my hand when the teacher asks a question. Mostly because I have to ponder ("introspect") it, and by the time I decide on an answer an extravert has already raised their hand, answered it, and the teacher has moved on to a new question. I hate it when teachers call me out of the crowd to answer because I require time to think when answering, which I am usually not allowed when under such constraints. Not to mention I can't think properly when the teacher and class are all looking right at me. Lame!
Anyways, I'm sure I can come up with some more key experiences I go through as an introvert, but these are the ones that came to my mind first. I'm not sure if they apply to all introverts 100% (I'm sure they don't), but I usually score as very highly introverted on any personality measure (Big 5, Eysenck's Personality Questionnaire, MBTI, etc.).
It's very interesting to me how some people are unable to decide if they are E or I. I think I have always known I was different from others in this regard, but it was a relief for me to know that there was a word for it: introverted. My mom referred to it as "anti-social" when I was young, or called me a snob for not being socially outgoing. I don't hold it against her because I understand where she was coming from.