Try not to laugh! If I can go from one European city to another on plane, on train, on bus, can I take a boat, not a tour boat, but a transportation boat from city A to city B?

And as I suspect this is true, how do I start a search on that? What do I Google? River transportation?

Oh, well, another one of my crazy ideas

I'd suggest you should start by looking at a map to see which cities are near one another and are linked by a river. Bear in mind that river boats travel at 10 mph or less (or perhaps 30 mph for a hydrofoil or other fast craft). You can, for example get a boat in summer from Köln to Bonn on the Rhine, or from Wien to Bratislava on the Danube. Once you have a journey in mind, then see if you can find if there is a boat operator doing this journey.

Thank you, Geoff!

very very few cities.

check out EasyBoat - plies rivers in Benelux and Germany i think and though is a cruise type ship it lets folks on for just lodging and transport - a backpackers River Cruise - had a link when i wrote of this once a long time back. Run by EasyJet folks - not sure of current situation.

For boats on the Rhein and on the Danube:

http://www.k-d.de/
http://www.ddsg-blue-danube.at