Using this as a category is almost unfair to the continent...but it is the only way to be comprehensive about what you can see and do there. I can certainly not go into detail of each country here, but there is so much to see and do, and honestly it would take multiple trips to feel you have seen Europe.
One of the world's oldest cultures can be found in Italy, and that is truly a starting point for many who wish to visit Europe. You have art, music, fashion and of course.....the food! There are numerous, wonderful cities in Italy, along with the countryside which is rich in it's own culture with wine growing, dining and a slower life of older days.
France is another “top” choice for those visiting Europe for the first time, with the strong influence held over arts, music and dining as well. With all the holdings that France has over the world, it is a major power in the world, and the French enjoy a rather high standard of living. It is a must stop on many of the romantic trips, with Paris being known as one of the most romantic cities in the world.
The Scandinavian countries offer sights, sounds and tastes that most of us only dream of. Stories of the Vikings are classics that we have all heard, yet many have not experienced it first hand. The smaller countries in central Europe hold long historical value and amazing scenes with their architecture.
And of course, the United Kingdom is probably most visited by Americans, as we have less of a language barrier there than other countries.
But, as you can see these are only highlights of a region so rich in history and culture that it would take months to see and do all that Europe and her countries have to offer.