This is a great question. It's also the basis for a personality test that I had to do when I was interviewed for my first aco****ing job. Which is very silly because in that setting you are going to leave out the more negative things. Anyhow....

For me, I see myself as kind of smart, emotional, kind of lazy, fat (I've actually lost like 85 lbs and am in pretty good shape now, still see myself as fat), lost potential, extremely shy, sarcastic, very opinionated, kind of self centered, feel like a burden frequently, troubled, a bad person, moodly and introverted. My Meyers-Briggs type is INTP, and is disturbing accrurate.INTP - Wikipedia, the free encyclopedia

How others see me, shy, very quite, smart (probably a bit of a know it all), emotionless, distant, reserved, a bit odd, amazed how i was able to lose weight (I have no idea what it means personality-wise, but it gets commented on a lot), aloof, opinionated, sarcastic, blunt, care free, or maybe just uncaring.

I think a lot of how people see me is based on how I have coped with my mental issues. I've built a very strong wall over the years, but it's probably not a good thing. Maybe someday I can dismantle it.