Audra and I took a life changing trip 3 years ago. We wanted to challenge the way we traveled, so we bought a flight to Amsterdam through Iceland, booked our stay in Iceland and our initial hostel in Amsterdam, and left EVERYTHING else unplanned. We didn't even have a flight home. Yes, we did some research: "Europe through the Backdoor" by Rick Steves and Nomadic Matt's Blog. We also had a vague idea of countries we wanted to visit, but that changed through the trip.
We learned a TON from this trip!
1) If you are doing an unplanned trip where you want to go to lots of places, get a Eurail pass.
2) In Brussels, we booked a train to "a random city in Germany" and received a ticket to Koln. We got off the train and recognized the Cologne cathedral immediately. Yes, cities have different names in English.
3) Don't wait until the last minute to book flights (usually).
4) The infrastructure exists all through Europe for this kind of travel. You can get off the train, find wifi somewhere, book a hostel, and start exploring.
5) The world was HUGE!!! We visited 10 cities in 6 countries and the world only seemed bigger after that.