How to get my own insurance
It made me
Feel secure 
"Don't procrastinate. Get this done!"
How I did it: I used to be insured through my parents. While this was fine (and cheap!) whilst I was a student and a recent graduate, I felt that now that I do have a serious and well paid job, I should get my own insurance. And it's not just health insurance either: I have my own apartment, so I had to insure that as well. All in all it ain't cheap, but it's worth it. Thank god I don't own a car...
Lessons & tips: Don't over-insure, focus on the things you know you will use. In my case: apart from the basic package I wanted extensive dental coverage as well as coverage for my eye wear (prescription glasses).
Resources: It's different in each country, I suppose. I used insurance companies' websites to compare various policies.
