In addition to all the great answers above:
Safety: Even if Europe is supposed to be safe, beware of pickpockets when being in the touristy areas, on markets, in the tube, in crowdy bars. This is a thing you should be aware of.
Also I like to keep a paper with copes of my ID, my health insurance and my visa card and important phone numbers deep down in my backpack (or suitcase if you don’t travel with a backpack) in case my wallet gets stolen.
Other Advice: ask locals what to do. Mostly you find a nice waiter or a guy that works in your Hotel/Hostel that knows the best way around the town. It’s ten times better than to rely on an outdated map.
Also in many big cities they have tours that are made by some freelance people. They are always great, because at the end you pay only as much as you like, depending on how much you liked it.
Good Places to Visit: If you are in Holland, take a train to Brussels. It is much faster, cheaper, interesting than taking a plane. They have awesome food (waffles, french fries) and the city is awesome.
I’d also say Paris is a must. Climb the Eiffel Tower to the second platform and then take the Elevator. It is like the best thing ever. Or do a night picnic in front of the Eiffel Tower, and watch the light show. (safety beware of the guys in front of scare coeur. They tie wristbands to your arm without asking an then you have to pay 10 bucks for them)
If you want to cover germany, go to Hamburg and dance a night through on the Reeperbahn (red light district with an enormous amount of clubs/bars/pubs), or visit Berlin with all its history. Or Munich – which is like cliché Germany.
If you’re going to Italy besides Rome I would advise you to go to venice. It is super expensive, but since the city is sinking it might be your last chance to see it ;).
A last general piece of advise: don’t run. don’t try to be in every city and don’t really see it. Just take your time to get to know the place you’re right now. If you do 10 cities in a week, you’ll be feeling like you have been nowhere. And keep a travel blog. They are great memories with pictures and everything. And a great way for your friends at home to see what you’re doing. http://www.fuzzytravel.com/ this one is free and easy to use.