The Danube Cycleway
The Danube Cycleway is Europe's most popular long distance bicycle route. It begins in Donaueschingen, Germany and ends at Sulina, Romania. The route used to end in Budapest, Hungary, so some older guides will only refer to the Donaueschingen-Budapest portion of the route.
One relatively cheap way to get to the beginning of the Austrian side of the cycleway from most of Europe is a budget flight to Bratislava, followed by train to Vienna, and then train to Passau. Then cycle to Budapest. From Budapest, you can get the train back to Vienna, and then another train to Bratislava for the return flight. Note that this route misses out the Donaueschingen to Passau section.
Renting bikes is often cheaper and easier than taking your own bike. The Copa Cagrana bicycle rental shop on Donauinsel, Vienna, offers a number of "trekking" bikes for €100 for two weeks, or €120 for three weeks. There are many cycleways for getting around Vienna, and bicycles can be taken on the Vienna subway.
The Cycleway is very popular with cyclists, and there are many rest stops, cafes, bars, and camp sites along the route.
Maps and other info
The "Danube Bike Trail" map series from Esterbauer are recommended. These can be purchased online. There are four books in the series, dividing the route:
The Danube Cycleway guidebooks from Cicerone are also recommended and cover the full route from Germany to Romania.