The first thing I did when I got my official diagnosis was to call my mother and tell her. She has had some mental problems herself so she can sympathize to some degree. She's often helping me with my welfare, meetings, doctors etc and she's happy to be included as long as I make an effort to be more independent.
My mother told my dad, and he didn't really know what it was. When he got some info on AS and a list of possible symptoms he said "If I read this five years ago I could've diagnosed you then", which really surprised me. He always tried to force me out of my room and threw my pc out at one point. He had big issues understanding my depression and difficulties, but now he's very supporting and he's very happy when I include him in my affairs and tell him how I'm doing.
I didn't like the response I got from my sister. All she said was "But you're not nearly as bad as my friend with AS, you don't seem to have problems at all." It made me feel like my AS wasn't important, because I can function well compared to some people with AS/autism. Compared to NT's I don't function very well at all.
All in all, I'm glad I told them. It's made my battle against my welfare office and other stuff much easier, and it's nice to have someone I trust with me to certain meetings as I have big issues processing all the information they throw at me.