Obviously, the answer to this question is going to vary widely depending on the circumstances of the individual responding to the question. I, personally, have been very lucky to this point.
In the United States, we have a system in which people typically get health insurance through their jobs (or through their parents until they reach a certain age). Not all jobs provide health insurance. You have to have a pretty good job (or a spouse with such a job) in order to get insurance. I have been lucky in that I have never had a worry in that respect. This may be because both my wife and I have graduate degrees and have been able to get good jobs.
To the extent that I have any worries, they have to do with what will happen when my wife and I retire. I wonder if Medicare will still be in existence. I wonder if we will be able to afford to buy health care while retired or if we will need to keep working past the typical retirement age. This is, however, much better than worrying about health insurance in the present. We have been lucky so far.