Adventure Activities

One of the things that is going to make your trips most memorable are the activities you do during the trip.

Amusement Parks
Of the top 25 amusement parks in the world, as per TripAdvisor, 5 are in Europe.

Europa Park - Rust, Germany (#7)
You can access this from Strasbourg, France.

Read more, here.

Tivoli Gardens - Copenhagen (#12)
This is right next to the station. So, you can leave your bags in the station lockers.

Disneyland - Paris (#13)
There is a special metro line that goes to the Disneyland from Paris.

Gardaland Park - Italy (#20)
This can be reached from Milan.

Other honourable mentions go to:
 * Asterix Park - Paris
 * Efteling - Amsterdam
 * Legoland - Berlin or Copenhagen

Aurora Borealis / Northern Lights
The northern lights are visible from September onwards and they get stronger from then. So, the later you go, the more your chances. The main factor of the visibility, however, is the weather. You need clear weather, no clouds and no city lights in order to see the North Lights.

The simplest way to see the Northern Lights is to take the train from Stockholm to Narvik. You can get down at Kiruna, Abisko, Narvik and see the lights from there. Upon reaching Narvik, you could even take a bus further to Tromso in Norway. The lights in Kiruna, Abisko and Narvik will appear close to the horizon. The Lights in Tromso will appear overhead.

You can also try to see the lights (though it's not advised) from Iceland or the Finnish Laplands in Santa Claus' Village.

Skydiving
Prague

Spain