Is it possible to travel through Germany/Austria/etc. by river "taxi" without signing up for one of the cruises such as Viking. My wife and I are potentially interested in taking a trip where we could cruise one of the rivers to a town, spend a couple of days, move to the next etc in a much less structured environment than the cruises. On previous trips to Europe we have rented a car and driven to destinations - we like to create our own tours. Any advise would be appreciated.
Several different ferry companies operate on each river. Some of these are listed in Rick's guidebooks for the areas he most recommends them, such as http://www.kdrhine.com/rhineschedule.htm for parts of the Rhine and Mosel. You could also try www.rome2rio.com for transport summaries, or just Google "Vienna Budapest ferry." Scenery is not equally fascinating at all points of your likely route.
You could of course include some trains in the mix, when you want to move faster. How to Look Up Train Schedules and Routes Online gives you the DB train schedule link and tips for using it.
Riverboats also travel up and down the Elbe river. A very scenic portion begins in the Meissen area and continues past Dresden into the Elbsandsteingebirge (sandstone mountains) with several intermediate stops. The one I checked out ends in Bad Schandau, near the Czechoslovakian border. You could get off for overnights. Schedules vary with the seasons. My brother spent a week in that area a couple of years ago in a b&b and loved it. He did have a car but also hiked.