The lack of responsibilities. No job. No bills. No money. No having to 'manage my time' (though I do a shit job of it, generally). No worrying about the future.
The optimism. I could do anything, be anything. Being a cynical, pessimistic arsehole may be more practical, but it sure as hell ain't as fun.
The friends. Many have moved away and I no longer see them anymore.
Agree with Adami: Late 80's and early 90's culture. Largely pop-culture really. The cartoons, the movies, the TV shows, and the absolutely ridiculous fashions. Most of it is still around in some fashion or another, but there was something about being in the moment with it, being there when it was big, when it was everywhere.
Not childhood, but more post-adolescence/early adulthood, but college. I loved college. I only went to a community college so this isn't nostalgia for dorm/party life, but just college and that time in my life. I loved just learning stuff. I loved how free I was to do almost anything I wanted (I had some money from my jobs, a car, and time), but I wasn't yet burdened by all the responsibilities of adulthood. I could hang out with friends every weekend until 4 in the morning, making midnight runs to Taco Bell, and playing Smash Brothers and Dungeons and Dragons until we could longer function. Many of my friends hadn't moved yet or gotten married and had kids so there was always somebody around to do something. See a movie, play some video games, or just something.