I've told my parents i think about three times over a period of time. The first two times, I didn't tell them the exact name of my disorder, just told them my behavior and how it affects me, and what others say about me, etc. But the first time i told them, I remember my dad just telling me to "get over it and be stronger" in a gentle way.
The second time i told them again, they were somewhere along the lines of "I thought you had gotten over it already." The third time I told them, I was serious about it and told them the specific name, which I think it's self explanatory: social anxiety, and told them all about how miserably it has affected me in daily functions, etc.
It was weird, but the next day they were acting super nice and cheery to me and treating me like a princess. Which was nice, I got a bit spoiled, lol. But anyway, telling them was like a thousand pounds off my shoulder.
I would never tell any of my friends though. Just my philosophy that people stay friends because the other has something to offer. Even best friends can turn their back on you. Everyone is selfish, so noone really wants to be around depressed, mentally ill people. I wouldn't really expose my great weakness to anyone else really. But that's just me.