The Independent recently published an articled titled "
50 things to do before you leave university". They have a nice list of things there, but I'd like to comment on some and add a few other ones from my own university town.
1. Walk over the arch bridge. In Tartu, Estonia, university town at its best, has an arch bridge. You are theoretically not allowed to walk over it, but I know very few people who actually haven't done it. I myself have done it probably 50 times and getting rather tired of it. Of course, people have fallen down, in one case the person was totally okay after falling down from the top. Fortunately another person softened the fall and broke her arm instead. But the number of people who have actually fallen down (without doing it deliberately) makes the bridge way more safe than driving a car.

Photo by DJ Sturm
2. As some have seen, the arch bridge is not only for walking over it. You could, for example, have sex on top of it.

Photo from elu24.ee
3. Now, back to non-Tartu-specific-stuff. Everyone should at least once fail an exam. If you're a true nerd and hate even the thought of it, come one, you go to the university just once in a life!
4. Have a learning marathon that lasts at least 50 hours. Even a wussy can do that! By the end of it, try to make sense of things and see how you're doing. If it still seems easy, add another 50 hours.
5. Teach foreign students your own language. My favorite words to each were 1, 2, 3, throw up!
6. Cook in a lecture. Not every lecture is very interesting, you've been there done that, sure of it. So why not take some *interesting* lecture like semiotics and do something that really shows you know about the signs and symbols and all that stuff. Gather a bunch of friends, take all the necessary ingredients for whatever you want to cook with you and, and start cutting, mixing and why not, once it's ready, eating!
7. Take a look at all possible lectures available in your uni. Rest assured, you will find some rather interesting ones totally out of your field of study. Things like bird watching or music listening or creating your own sms service - these are just a few good examples from my own experience.
8. Every student needs money to survive. Beer is needed for survival as we all know. And you can't always expect your parents to help you out here. After all, university is the preparation for life and you need to start earning money. So think what you'd like to do for a bit, and contact companies saying that you don't really want to work, but as you need money for beer, you are willing to do them a small favor and work for them a bit in exchange of some beer money. And of course, you want a flexible schedule and you don't want to work much. Obviously, that's the way you *usually* shouldn't contact the employers, but after all, it's university, time to try stuff. It worked for me, got me some beer money!
9. Drink the the whole night and still go to the lecture. But try not to fall asleep. Or why not, do. One professor is still saying high to me on the street, only because I managed to fall asleep in an auditorium on 200 people, but on the first row.
10. Don't drink for a month. Now that's a challenge for you!
11. Visit the guest nights of all the student organizations out there. Free booze is always good. You don't have to join them, but it's still good to drink for free.
12. Write for a university newspaper. To make it more fun, be against the publisher of the paper and still get it published. Tried that, great success! Of course, my career, as expected, ended with that article there as well.
13. Dress up with friends and have a run around the classrooms while the lectures are on! Have an announcer to present you. You can can dress up as any one or any thing. Your creativity is the limit.
What else COULD a person DEFINITELY do before leaving university?