It's similar in the UK- at 18 you're legally an adult. However, if you're still in school doing A Levels when you turn 18 it makes no difference apart from the alcohol thing, since you're still in school, living with your parents etc. If you're not still at school, you will have left at 16 so (again apart from alcohol/clubbing) it's not going to make a huge amount of difference either.
When you leave home is a much bigger deal and more of a true "coming of age" thing.
As for my own experience, my birthday's in October so I turned 18 right at the beginning of my final year of school. I went to the pub, some people bought me drinks (not really a big deal since being underage really doesn't stop people consuming alcohol) which was nice of them. And then yeah, I got on with school, exams and all that jazz, same as before. Voted in the general election a few months later. In terms of everyday life I guess it was kind of cool that my parents didn't have to sign permission slips for stuff any more, but that was about it.
EDIT: if you're working you're entitled to a higher minimum wage in the UK too, so I guess that's the main benefit of it.