It was in the early morning hours, still and silent, when I slipped out of bed and drew back the curtains on our balcony window. In the darkness, the ship's hull lights cast a yellow glow on the dark, rushing river, betraying just how fast we were skimming through Austria's historic Wachau Valley. Inside, snug and warm, I lay back down and was rocked back to sleep by the gentle rolling motions of the ship. A few hours later, I opened my eyes to see the 12th-century Schönbühel Castle appearing out of the mist like a mirage.

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Just another day on the Danube, the second-longest river in Europe and street address for dozens of historical towns and villages along its banks. The Danube flows from the highlands of western Germany to the Black Sea, nurturing cultures, cuisines and civilizations along some 1,800 miles. And what better way to sample these offerings—or those of the other mighty rivers of the world—than to sail on big, specially designed vessels that move you from port to port with no fuss and hardly a bump?

River cruising is one of the great travel-industry brainstorms of the past two decades, says Richard Turen, owner and managing director of vacation planners Churchill & Turen Ltd., and the market is growing about 16 percent a year. There are river cruises in the U.S., Europe, Asia, Africa and South America, led by 20 or so companies large and small, each of which offers specific charms and peculiarities.

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Last October, my wife, Nichol, and I—first-timers to any type of maritime vacation—spent seven days on the Danube. We set sail from Vienna; headed east to Bratislava, Slovakia; and then traveled upriver, making stops in towns and villages in Austria, Germany and the Czech Republic. Our home for the week, the newly commissioned Savor, is part of a nine-ship luxury river-cruise line started by Tauck, a well-regarded Connecticut-based touring company that's celebrating its 90th year of providing all-inclusive tours. The vessel, nearly as long as one-and-a-half football fields, was designed for comfort—outfitted with a gym, massage room, hair salon and lots of convenient touches, including Nespresso machines and U.S.-style 110-volt electrical outlets in each cabin, to charge phones and iPads. On the top deck, an outdoor hot tub and putting green beckoned those willing to brave the cold European fall.

Our tour began on land, in Vienna, where Nichol, I and 128 of our fellow travelers spent our first evening together at the Palais Pallavicini, a baroque 18th-century palace where Mozart and Beethoven flattered their wealthy patrons. During a wine-soaked five-course dinner beneath magnificent gilt-and-crystal chandeliers in the Great Ballroom, a local chamber orchestra presented a buffet of kultur Viennese-style: string pieces by Beethoven, Mozart and Strauss; a few operatic duets; and a ballet pas de deux or two to boot. Judging from the whoops, we were an appreciative bunch of culture-vultures. I surveyed the room. It seemed to be largely populated by energetic retirees, mostly experienced travelers, whose average age I would guess to be in the mid-60s. Arnon Reichers, 65, a willowy retired college professor and veteran traveler from Columbus, Ohio, summed up the evening for all the revelers in a single word: "Spectacular."

See also: 5 American river cruises

Following a couple of days of motor coach touring in the Vienna Woods, Baden and other destinations, we were eager to set sail. The Savor's 47-person crew welcomed us aboard for an ambitious first-night dinner, including a memorable mushroom cappuccino soup beneath a cloud of creamy white froth. My wife has food allergies, and the staff made every effort to keep her well-fed and healthy and was successful close to 95 percent of the time.

Then the river beckoned. Our first stop was Bratislava, a lovely 10th-century town with more "Original Slovakian" restaurants than is likely to be true. It was a Saturday, and even in the chilly weather, riverboats were double- and triple-parked at the riverbank. Bratislava is a popular port for most of the river-cruise lines, and it can get crowded by midmorning. We passed up the guided tour and did our own walk around Old Town, quirky and charming, with lots of public art, including a statue of one of conqueror Napoleon's soldiers in the main square; according to area lore, he fell in love with a local girl and stayed behind.