Germany isn't short of them, but Hamburg is home to the country's highest concentration of millionaires. At the same time, it has one of its most vocal alternative cultures. The Szene (Scene), as the Germans call it, is responsible for the most famous squat in the world, the Hafenstrasse, a section of housing down by the harbour which the authorities (armed) have tried to storm several times and failed. The Szene is also responsible for urban meadows of graffiti on the U-Bahn (Tube); a vigorous cafe life; and some of the largest technopark gatherings in the world.
Meanwhile, the millionaires can enjoy some of Germany's finest malls, world-class music, and a surfeit of yachting clubs and luxury hotels.
Hamburg (the name derives from Hamm, or "marsh") grew up in the Middle Ages as one of the main cities of the Hanseatic League, a loose trading alliance between cities of the Baltic coast formed for protection against pirates.
At its height, the League spread all the way from Dinant to Cracow, from Novgorod to Dresden. The representatives of the Hansa towns met each year in Lubeck to deliberate on such matters as anchorage, a naval force to protect against aggression, and a common currency (the euro, mark 1?). They built one of the world's most successful commercial unions, trading in herring, furs, spices and steel before succumbing to the general southward shift of world trade with the discovery of the New World. At the same time, the herring shoals on which much of their fortune was based, decided - for some fishy reason known only to themselves - to uptail it from the Baltic to the North Sea.
Now, the Hanseatic League consists of a rump of Hamburg, Bremen and Lubeck. The citizens of these towns still proudly display HH, HB or HL (Hansestadt Hamburg, Bremen etc) on their number plates. The legacy of the League is apparent in the concentration of financial services in Hamburg, and many of the big names of the old merchant class still control the city's politics. But this class is now being challenged by the growth of younger media and publishing industries, giving a new spin and verve to the city's old true-blue culture.
First impressions are of a wide watery place with no focus. A town- planning policy of planting 2,000 trees every year has resulted in a city divided into one-third trees, one-third lakes, and one-third buildings. Add to this the fact that a great fire in 1842 destroyed much of the old city, and you have a diffuse and strangely ghosted urban architecture. There is the odd gabled merchant's house or warehouse standing like a post-modern comma in the middle of concrete parentheses to remind you how beautiful the city centre must have been, and you can see a townscape in the Kunsthalle. But mostly it is gone.
If there is any centre at all, it is the Ratshausmarkt, where the town hall presides over a large square. It is an overblown late 19th-century affair of gutted rainforest and gilt where the elders have had themselves extensively painted in the style of 16th-century doctors, with velvet breeches and ruffs. But the scene in front of the Ratshaus is far from pompous: a mass of stalls selling charcoaled bratwurst, rindfleisch (beef) and beer, and every kind of new-age crystal-seller and healer displaying their wares and offering their services.
Leaving the market square, there are a number of smart shopping malls which run between the canals. Hamburgers are very proud of their malls and it is not hard to see why when you imagine the city before the arrival of international consumerism. It must have been a bit like Glasgow, in the grip of apparently terminal decay as the shipyards of Europe gave way to competition from Japan and South Korea. But shops have done what ships could no longer do: created an atmosphere of joie de vivre and luxury in the once gloomy quarters of the canal.
Sooner or later you will have to pay your respects to Hamburg's raison d'etre: the water. You can do this in two ways. Setting off from the jetties of Jungfernstieg, close to the shopping area, you can take any one of a number of somewhat voyeuristic tours of the Aussenalster lake where the millionaires live. The boat slows lugubriously before each stuccoed villa with its yacht moored in front of it. And the engine is cut completely in front of the international hotels which line the lakeside while the guide makes sure we are all in possession of vital information: the hotel is "zwei hundert sieben und siebzig meter breit", "hundert fierzig meter tief" and cost "zwanzig tausend drei hundert dreizig millionen von mark" to build.
Better value is the harbour tour which leaves from the Baumwoll to the south of the Ratshausplatz. You set off on a choppy tug with an old Hansa tar at the tiller. Containers from Iran, Kuwait, Riga, Sebastopol and Cadiz stand in the docks with their bilge-holes spouting water from long ocean voyages, while a few sailors are lowered by rope on narrow trestles (not much in the way of safety regulations here) with a pot of paint and a brush to repair the rusted lettering of the once-proud names.
The tour also takes you past the Speicherstadt, or warehouse city. This was established in 1874 when Bismarck insisted that Hamburg (still a free city) join the German Customs Union, which would make the city liable for duty on all incoming goods. The Hamburgers promptly built a warehouse complex just outside the city walls to escape the Prussian tax. Now the warehouses loom above the harbour canals with grim red-brick walls and narrow green doors giving nothing away. But inside there is still tea, coffee, spices - and oriental rugs, of which Hamburg is Europe's largest importer.
The merchants of Hamburg have always been good to the arts and while you are here it is worth paying a visit to the Kunsthalle, or art gallery, which has works ranging from Fra Filippo Lippi to Rembrandt, and a major collection of 19th-century German Romantics. More exciting perhaps is the new Gallerie der Gegenwart (gallery of contemporary art) designed by Cologne architect Oswald M Ungers. It is a giant cube of granite and glass overlooking the water, with interactive displays and a collection of post-1960 American and German art to equal any inside.
Hamburg wouldn't be Hamburg without its notorious nightlife, centred on the Reeperbahn (ropemaker's way), a quarter-mile strip of burger joints and amusement arcades to the West of the civic centre. The nautical name is a clue to an atmosphere that still prevails: one of rough-and-ready commercial sex. The city has tried to clean up its act and a lot of it now takes place behind closed doors.
But the oldest trade in the world is on frank display in St David's Strasse, which runs from the Reeperbahn down to the harbour. The women have a distinct uniform: trainers with two-inch soles, black leggings, bomber jackets and money pouches slung across their front. They stand for long periods among the milling crowds and then move in with killer precision on any single man with a worried expression on his face.
While you are in the Reeperbahn, don't miss Freiheitsstrasse, where the Beatles made their debut in a strip club. Their families thought that they were doing a turn in some jolly German music hall.
If you are after more sophisticated nightlife, Altona is the place. A once-shabby area of turn-of-the-century blocks, now going busily upmarket, it has good jazz at the Cotton Club or the Fabrik, and art-house films at the Filmhaus, a former factory for making ships' propellers. Altona was owned in the Middle Ages by Danes who granted Jews the right to settle there. Now it has strong Turkish and Greek populations, and while the young and trendy meet in the cheap and delicious eateries, Turkish men sit and smoke at dusk in the station square, surrounded by buckets of ranunculi and lilies.
Gill Airlines (tel: 0191-214 6666) offers return flights from London Stansted to Hamburg from pounds 89, flying in a romantic ATR42 turboprop plane. Scandinavian Seaways (tel: 0990 333000) runs ferries from Harwich. The journey takes 24 hours and the cheapest fare of pounds 57 return is for stays of up to four nights. Book 21 days ahead.
Where to stay
Top of the range is the new Hyatt Hamburg (tel: 00 49 40 3332 1234) on Monckebergstrasse - the peak of luxurious minimalism, with the city's main attractions on your doorstep.
Cheaper hotels are clustered round the Hauptbahnhof, such as the Annenhof, Lange Reihe 23 (tel: 00 4940 243426) and the Helga Schmidt, Holzdamm 14 (tel: 00 49 40 280 2119).
The Hamburg Travel Ticket, from the tourist office, costs DM26 (pounds 10) for a single (DM42 for a family) and entitles you to free public transport for three days, and reductions on galleries, city tours and lake cruises.
German Tourist Board (tel: 0171-317 0908); Hamburg Tourist Office (tel: 00 49 40 300 510).