If you're worried about getting sick while traveling, rest assured: Most of Europe offers high-quality medical care that's as competent as what you'll find at home. The majority of Europe's doctors and pharmacists speak at least some English, so communication generally isn't an issue.
Nearly all European countries have a universal health care system. Though some people refer to it as Europe's "free health care" system, in reality, it's not really free. While each country has its own variation, the common denominator is that everyone pays for health care as a society — intending to minimize the overall expense and spread around the cost and risk so that an unlucky few are not bankrupted by medical costs. This also ensures that those living in poverty can get the care they might not otherwise be able to afford.
Luckily, I've never been seriously injured while traveling in Europe. But I hear countless tales about travelers needing medical treatment. One person told me about how she sprained her ankle during a visit to Denmark. She was X-rayed, bandaged up, and given a pair of crutches to use. The hospital did not ask her to pay a dime — only to return the crutches when she left Denmark. And a staff member of mine, whose infant son received excellent care after a lung infection in France, came home to declare, "Anyone who says socialized medical care is subpar hasn't seen it in action."
While no system is perfect, Europe's universal health care does mean that everyone is taken care of — including foreigners. So if you get sick or injured while traveling, you will receive treatment, no questions asked.
If an accident or life-threatening medical problem occurs on the road, get to a hospital. For serious conditions (stroke, heart attack, bad car accident), summon an ambulance. In most countries, you can call 112, the European Union's universal emergency number for ambulance, fire department, or police. Most countries also have a 911 equivalent that works as well. Or you can ask your hotelier, restaurant host, or whoever's around to call an ambulance (or a taxi for less dire situations).