On my small group tours, we always act in a safe and cautious manner. Here are my tips for a safe trip:
Stay Away from Lines: Large groups congregating on lines always makes me nervous. In the airport, I have TSA pre-check to get me into the secure area quickly. I buy VIP, no-wait-in-line admission to museums to get into secure areas of museums quickly. I travel off-season to avoid crowds.
Protect Valuables: While violent crimes are rare in Europe, pick-pockets and petty thievery is more common. No need to be obsessive about it, but protect valuables, don't wear flashy jewelry, don't talk to strangers who randomly walk up and ask you to complete a survey, ask if you speak English, or hand you a gold ring or other item. Always use ATM's when accompanied by another person. Don't walk around with large sums of cash. Leave your passport at the hotel.
One of the leading causes of death and injury in Europe are pedestrian accidents. Please note drivers in Europe do not give pedestrians the courtesies often extended here in North America. Besides, in some countries they drive on the other side of the road. My advice is to not jaywalk and ALWAYS look both ways before crossing the street. Don't trust any vehicles.
Some travelers have chosen to travel to the safest country in the world: Iceland.