There are many options for individual (as in non-group, not as in non-family) health insurance, although to avoid the hassles of what you're talking about you might have to think outside the box. A typical major medical policy will increase premiums if you start to have medical problems, and if you try to switch you have to deal with "pre-existing conditions."
There are other options, but they work differently and seem scary to most people who are used to letting the company deal with it at a first glance.
Source: I was a health insurance salesman for a short period of time, and was licensed to sell for most of the insurance companies out there. It's part of why I'm not scared of going out on my own and freelancing -- I know enough about how insurance works not to worry about it, and can even sell myself a policy and get commission. However, it's been a couple of years, and I probably can't give you accurate, detailed information -- many of the insurance companies are revamping their business models and policies in anticipation of Obamacare.