This river is an impressive 1094 kilometres long, flowing from the heart of the Czech mountains to the North Sea near Hamburg. Few beyond central Europe are familiar with its name, but cities along its banks include Dresden, the porcelain centre of Meissen, and Wittenburg, linked to the story of Martin Luther and the rise of Protestantism. Such ports of call provide cobbled old towns, Gothic cathedrals and baroque palaces, while the landscape of the Sandstone Mountains, nicknamed Saxon Switzerland, provides soaring cliffs. Cruises generally run between Hamburg and Prague on the Vltava River, a tributary of the Elbe.

2 BRAHMAPUTRA RIVER, INDIA

This huge river tumbles down from Tibet through Assam and Bangladesh before ending up (after changing names numerous times) in the Bay of Bengal. Cruises usually travel between Jorhat and Guwahati before veering off onto the Ganges-Hooghly and finishing in Kolkata. Like the Ganges, the river's lower reaches are sacred to Hindus. It's the only river cruise providing views of the Himalayas and also stands out for elephant safaris – not exactly your typical shore excursion. National parks, monasteries, tea plantations and tribal villages are other attractions of this river cruise truly off the beaten track.

3 LOIRE RIVER, FRANCE

The Loire Valley, which runs west of Paris and is famously dense with chateaux, is well-known, but few realise you can cruise along this glorious section of France's longest river; only last year did Loire Princesse become the first cruise ship to operate here. The Loire offers an itinerary dizzyingly dense with history and culture, round trip from Nantes. Cruises visit the shipyards of Saint-Nazaire on the Atlantic Ocean, Muscadet wine country, and charming medieval towns such as Clisson. Highlights are the fine city of Angers and the fabulous chateaux of Villandry, Azay-le-Rideau and Usse.

4 SNAKE AND COLUMBIA RIVERS, US

And now for something completely different: cruises through the Pacific Northwest, some on replica paddlewheelers. Ships sail between Clarkston on the Snake River in Washington state to Portland in Oregon, one of the West's most lively cities. Many cruises are themed around explorers Lewis and Clark, who explored this region in 1805. Highlights include historic Fort Clatsop, a visit to a working ranch, volatile Mt St Helens volcano and Columbia Valley vineyards. Landscapes are magnificent: along one stretch of the Columbia River, gorges cut through the Cascade Mountains, overlooked by snow-capped volcanoes.

5 RED RIVER, VIETNAM

This lengthy river rises in southwest China before flowing into northern Vietnam, right through Hanoi and into the Gulf of Tonkin. River cruises meander up tributaries such as the Lo, Da and Khin Thay rivers too before taking in Halong Bay and its famous rock pinnacles. The few cruise ships that sail here take passengers right into the Vietnam highlands, where the scenery is a dramatic mix of shimmering rice paddies and limestone rock formations. Water-puppet shows, ceramics villages, old temples and local markets make for countryside visits, providing a good contrast with a day in frenetic Hanoi.

6 PO RIVER, ITALY

The Po flows across northern Italy for 652 kilometres and is difficult to navigate, fluctuating wildly in water levels. Still, a few cruise companies nudge some 60 kilometres inland from Chiogga on the Venetian Lagoon as far as Polesella. In truth, the Po River landscape is rather drab, but you could hardly complain about the shore excursions: Verona, Padua, Bologna and Ravenna are among Italy's loveliest towns. Cruises also spend plenty of time on the Venetian Lagoon, starting and finishing in Venice: few cities are better suited to admire from the intimate decks of a river-cruise ship.

7 KWAI NOI RIVER, THAILAND

If you know this river, it's probably for its Japanese WWII prisoner-of-war camps and the classic 1957 movie Bridge on the River Kwai. The bridge marks the point where the Kwai Yai and Kwai Noi rivers merge at Kanchanaburi west of Bangkok. This is a short river cruise (just three or four nights) but packs in sights that include Buddhist caves, Khmer temples, a tiger sanctuary and former Australian and British POW camps and war cemeteries. Lush scenery is studded with waterfalls tumbling off cliffs, and the river provides ample opportunity to swim, raft and kayak.

8 ODER RIVER, GERMANY/POLAND

The Oder rises in the Czech Republic, partly creates the German-Polish border and empties into the Baltic Sea at Szczecin (or Stettin) in Poland, an important Hanseatic trading city in the late Middle Ages, and surrounded by traditional fishing villages. Most of its length is navigable, making this historically an important trade route into central Europe. Cruises meander through the scenic Oder Valley National Park and past UNESCO-listed moors rich in waterbirds. Cultural highlights include the gothic architecture of Brandeburg, abbeys and monasteries, and Berlin, reached from the river port of Henningsdorf on a day-long shore excursion.

9 CHINDWIN RIVER, MYANMAR

To call the Chindwin a mere tributary of the better-known Irrawaddy River is doing it something of a disservice, since the Chindwin is over 1200 kilometres long and impressive in itself – though rather shallow, making navigation tricky and seasonal. In the dry season, cruises run between Monyaw and Homalin, getting as far as Hkamti during the monsoon. For bragging rights about remoteness you could hardly do better: you even need special permits to visit the region. Beautiful cave murals, Buddhist statues and traditional craft villages dot the riverbanks, flanked by lush farmland and forested hills beyond.

10 OHIO RIVER, US

Step aboard a river ship at St Louis on the Mississippi and sail east across four states of the American heartland on the grand Ohio River that was so central to opening up the West; the port town of Cape Girardeau in Missouri has a 250-year trading history. The scenery is particularly stunning through Kentucky, where Louisville (noted for its horse studs) has a great 11-kilometre riverside walk. Cruises finish at Cincinnati, one of the Midwest's most attractive cities, with its distinctively German 19th-century core, great open-air food markets and fine views over the Ohio River.