Assuming you’re going as a tourist, with a round-trip airline ticket you don’t “need” any type of insurance to go to Europe — at least in the sense of insurance being an entry requirement to get into any country.  If there’s some reason (like a one-way airline ticket) that the immigration agent who checks your passport on arrival thinks you’re trying to sneak into the country to work or stay long term, you might be asked for proof of financial resources and health insurance — but that’s almost unimaginable if you have a round trip ticket. 

You will need insurance if you rent a car, but that’s part of the rental package.  You may want special trip insurance to cover emergency medical care (your regular health insurance may ultimately reimburse at least part of your costs), emergency medical evacuation, baggage (lost, delayed or damaged), trip cancellation or delay, expenses associated with missed connections, etc.  Check with your insurance agent, AAA or a travel agent.  You may have some of this coverage through your major credit card, bank “service package,” auto club, etc. so check to see what you have and seriously consider what you really need before buying more. For example, if a death in the family or illness prevents you from going on your trip, cancellation insurance will pay any non-refundable expenses.  However, you can usually change the date on your airline ticket for $200 to $300 and many of your hotel reservations will be refundable, so you don’t necessarily need thousands of dollars worth of trip cancelation insurance.