What is likely the most important factor is your employment status, and the kind of place you work for. The best thing to have these days is full time employment with a company that offers some kind of health plan as part of its benefits. However, that may be changing soon, as prices go up and companies are increasingly worried about their bottom line. The best thing you can do to protect yourself is stay abreast of current information about your company, and what they plan on doing in the future. That way you'll about any changes before they happen.
One more important factor that can drastically reduces your chances of getting insurance on your own is a pre-existing condition. It is difficult to get coverage, or the coverage you do get will cost you plenty, if you have any existing health condition. If you do have an existing condition, and are currently covered by your employer's plan, treat your job like gold. The insurance you are getting through your work may be much more valuable than you realize.
Another thing that can make it exceedingly difficult is if you've ever been denied coverage in the past. This is a warning sign to insurers that you may be a high risk factor. So even if you do qualify for coverage, it may cost much more than you are willing to pay. If you have been denied coverage in the past, there's not much you can do now. One way to prevent it from happening is to not abuse your insurance, and reserve it only for emergencies, or genuine health needs.
Without question, the days of cheap insurance that covered everything and everybody are long gone. Insurance is going to get more expensive, and coverage is going to get more limited. You need to take a proactive stance, and always be shopping around for a better deal.