In Finland it's a huge thing (even with free higher education). Not everyone goes to high school (it's around 50 % I think) and though people get celebrated for graduating from vocational schools too, it's very low key compared to high schools.
I know that other countries have school leaving exams too and they're probably as hard as ours are but for some reason ours get a lot of attention. The questions get posted in newspapers (the next day) and when the results are announced there are stories about students who have done particularly well. This year there was a girl who got the highest grade in nine subjects, though many people take less exams. The system has changed and now it's possible to take more (in my time all sciences got lumped into one exam) but in my time taking four or five was common, you had to take at least four (mine were Finnish, Swedish, English, German and Maths). School years ends in February for third year high school students, there's some traditional celebration then (with other students), then there's a month's study leave for last minute studying and then there's the exams. Languages have two parts, listening comprehension which takes about an hour and a written exam that takes all day, for Finnish is two written exams (again, you have the whole day for each) and for Maths one exam, I think that these days other subjects (like chemistry and history and biology) get half a day each. You don't have to do the whole thing at once, you can take some subjects in the fall and some in spring. It can be quite easy, as it was for me, I passed easily with good enough grades but if you want to do very well you usually have to study a lot. Most universities have entrance exams but you will get points for your grades and sometimes with good enough grades you don't have to take the entrance exam.
There's a graduation ceremony at the school, usually only family goes there (because the seating is often limited and it's boring), there will be speeches and maybe some performances and it my school there was something involving men who had graduated there 50 years ago (when it was a boys' school). Then the students get called one by one and receive their diploma and the hat. The hat is very different from what I've seen used America, it's a remnant from a time when university students had to wear uniforms and it has a lot of symbolic value. Being a high school graduate used to be a big deal and it wasn't possible for most people, so people were very proud of them in their family and the students (they are called ylioppilaat, "high students") might wear the hat all the time. These days the hats only get worn at May Day, which is a student celebration here. This
is what the hat looks like, with typical graduation fashions and singing. (and this
was me, 13 years ago at my graduation with my mother).
After the ceremony at the school there's usually a celebration at the students home. The guests are usually family, maybe family friends and possibly friends of the student if they aren't at their own parties. It's also not uncommon to invite teachers, for some reason I invited my art teacher and she actually came to my party. There are also gifts, money is the most common but you might also get gifts that are meant for your new independent life, like sheets and dishes and things like that. And I got a lot of roses. Some people may go partying with their friends later. And then you get a professional photo taken and send it to your relatives and they display it in their bookcase.
There are smaller ceremonies for other school levels but there usually isn't much celebration connected with them. School year always end with a ceremony/assembly thing, with performances and singing and there's usually something involving the class that's leaving the school. I think that at one school we were given roses and at another our diplomas. There's no formal kindergarden here so no graduation for that.