I do not know if you consider Russia to be part of Europe but here are simple tips for those curious and brave enough to ever come here.
Forget everything you learned about crossing roads. France has the highest in Europe rate of fatal traffic accidents. Still, in Russia the rate (per capita) is 3 times higher! There are about 60000 deaths per year!
When you cross the street, look to the left, look to the right. If there are no cars visible, you can cross safely. If there are cars, wait until they all stop (they should do it if it is a crossing and there are traffic lights) and then cross. If you are jaywalking, try to avoid the cars. Run if you have to. It is considered polite for pedastrians not to cause any inconvenience for cars.
Beware the cars that are turning at the crossroad. If you see a green light, that only means that cars going straight on the street you are crossing have to stop. The cars that are turning to this street and have to cross your path will not let you go first. Either run or wait for them to go. Look at other pedastrians. No driver would want to kill several pedastrians at once - that will get them in serious trouble. Use the kids, old people and mothers with baby carriages as a cover (I am serious). Use the trams and other cars as a cover whenever possible (again, I am serious - no driver would want to hit a tram).
A few weeks ago I was crossing a street and a car didn't stop. It just slowed and slightly pushed me. I was quick to get away from it, but it would be pointless to argue with him afterwards or call for police. :(
Avoid bad drivers. If you see a black BMW ignoring the red light at the crossroad, do not expect him to stop when he sees the pedastrian crossing the road (although, most will make some effort to avoid killing you). Be especially aware of "8" and "9" models of VAZ (see http://www.vaz.ru/imgs/news/miniphoto/_2108.jpg). These cars were introduced in early 90-s and many of them were bough by those Russian who got some money at that time - not all of them criminals, but anyway. Drivers that have older cars usually learned to drive in USSR, when situation was much better. Drivers that have newer cars are those who earned their money recently, when Russia is a more civilized place. Many of them are relatively lawful middle-class people that sometimes show some respect to pedastrians.
It is considered a bit dangerous for Russian to spend a lot of time in the West, because they might lose their caution and be hit by a car when they are back.
Good luck!