I couldn't wait to be grown up and independent, and mostly it hasn't disappointed! I agree with @BemidjiMinnesota about simply wanting control of my life, which you don't have as a child. Things I looked forward to were:
@LisaSimpsonsbff I agree about the (mostly) not having to own up to losing or breaking things. If I do have to do this as an adult, I still feel the childhood fear.
Not being talked down to by adults: I felt that some adults (such as shop staff) did this to children, simply because they were children.
Not being bullied. I know that adults aren't always free of this, but in my experience it happens much less when you are an adult, and you have the tools to deal with it, instead of the "just ignore them" I always heard as a child.
Having my own keys.
Being able to wear designer trainers, and without socks: I was forbidden to do both (until I was able to buy them myself). I have loads of them now, and wish I had more feet on which to wear them!
And a silly one: being the person who was in charge of party games, instead of taking part in them. I wanted to be the one who was blindfolding the guests and spinning them round so they could pin the tail. As a teenager, I did once get to do this, having declared myself as too old to pin the tail myself. 