The Free and Hanseatic City of Hamburg has been Germany's second-largest city since Vienna no longer belongs to Germany (i. e. 1866). This position was cemented when Hamburg (north of the Elbe river, built around the Alster river), Altona (west of Hamburg), Wandsbek (east of Hamburg) and Harburg (south of the Elbe river and Hamburg) were united by the Groß-Hamburg-Gesetz (Greater Hamburg Law) of 1938. Hamburg also is the second largest city in Europe (behind St. Petersburg) that is not a national capital. Although it is technically not a coastal city and a good 60 miles away from the North Sea, it has a quite maritime flair, also due to being a traditional Merchant City and former part of the Hanseatic League, and Europe's second-largest seaport because big sea-faring ships can sail up the Elbe river.
Foreigners and fiction often reduce Hamburg to its Red Light District which is referred to as "Reeperbahn" (the main street that goes through it) everywhere outside Hamburg and "Kiez" by Hamburg's citizens; justified in that sailors who used to be the largest group of foreigners to come to Hamburg went there straight from the nearby seaport and actually didn't see much more of the city in the first place. Unlike certain rumors, prostitutes and brothels don't line up along the Reeperbahn anymore—it's the Herbertstraße where they do. Also, it's there (although not on the actual Reeperbahn) where The Beatles started their career in 1960.
However, there's a lot more to Hamburg.
The Hauptkirche (main church) St. Michaelis with its clock tower, nicknamed "Michel", is Hamburg's most famous landmark. Fiction sometimes uses it for the Eiffel Tower Effect.
On the same street but more to the east, the St. Nikolai Cathedral of which only the tower remains after the World War II bombings. It was another one of the five main churches and the tallest building in the world from 1874 to 1876.
Further famous landmarks around the harbor area include the Elbphilharmonie (under construction), the St. Pauli Landungsbrücken, the Lion King musical tent and a few times every year the HMS Queen Mary 2. Landungsbrücken and Queen Mary 2 are often used for the Eiffel Tower Effect on picture postcards.
The building of the Hochbahn (what Hamburg calls its Underground, Subway or El, whatever you're used to) through the Altstadt (Old Town) left a gash which grew into one of Europe's most famous shopping streets, the Mönckebergstraße, which stretches from the Hauptbahnhof (main station) at its eastern end to the Rathausmarkt (town hall market) at its western end. Another one, the Spitalerstraße, branches from it.
Parts of Hamburg seem like a City of Canals. All buildings in the Speicherstadt (Storage Town) have one canal side and one street side. The Alster river is mostly a canal or system of canals in Hamburg except for the artificial lakes Binnenalster and Außenalster. Further canals extend from the Außenalster. It's no wonder that Hamburg has more bridges than Venice, Amsterdam (two rightful Cities of Canals) and London combined.
Hamburg's biggest bridge, the Köhlbrandbrücke, is a famous landmark itself and the only bridge under which sea-faring ships up to a certain size can pass. Actually, crossing the Elbe river is difficult due to the large ships which have to be able to go everywhere. There are two tunnels, one with elevators connecting the Landungsbrücken with the harbor itself, and one as part of the Autobahn A 7, there are bridges in the east where no sea ships go anymore, and Hamburg's public transit includes several passenger ferry lines.
The Heiligengeistfeld (Holy Ghost Field) is a large free area to the east of the Reeperbahn. That is, 25% of the time, it is not free but occupied by northern Germany's largest fairgroundwhich is called Dom. "Dom" translates to "cathedral" and tends to confuse foreigners and even other Germans who sometimes expect a large church. Then again, the Dom was named after a church which used to stand in this location. North of it stands a humongous bunker, a Flakturm, which now contains studios, a music club and a big musical instruments store.
Soccer is Serious Business in Hamburg—in all of Germany, actually, but even more so in Hamburg. You support either the Hamburger Sportverein (HSV) or the FC St. Pauli, but never both, even if they rarely play in the same league. The more successful HSV is the only club in Germany that has never been below the First Federal League, but St. Pauli has a worldwide following due to the alternative culture it represents.
Residential areas in Hamburg range from concrete ghettos (Steilshoop, Mümmelmannsberg, Kirchdorf-Süd etc.) to luxury quarters (Blankenese, the Elbchaussee, but also the areas around the Außenalster). That said, housing in Hamburg is always expensive. Not Lower Manhattan-expensive, not City of London-expensive, but expensive. Constant gentrification of attractive and formerly comparatively cheap cult quarters with old, unmodernized houses (Schanze, St. Georg) doesn't help, nor does the construction of new residential zones which almost always end up in the premium class. At the same time, Hamburg has 1.4 million square meters of vacant offices, and new office buildings keep popping up everywhere.
There are numerous green recreational areas in Hamburg. Among the biggest is the world's largest park cemetery in Ohlsdorf which is twice the size of Monaco. The actual Stadtpark in Winterhude isn't small either.
Hamburg speaks its own German dialect named Missingsch which is described as "when a native Low German speaker tries to climb up to High German/Standard German but keeps sliding down into Low German." The latter (a.k.a. Plattdeutsch) is known in Hamburg, too, with a variety of subdialects. In fact, the Ohnsorg Theater has its own Plattdeutsch dialect.
By the way, the Hamburger is actually named after the city of Hamburg. It was invented by an emigrant from Hamburg who modified and refined something called "Rundstück warm" in Hamburg: a bun with a slice of roast and gravy.
Hamburg has been considered (one of) Germany's most cosmopolitan city since the 17th century at least and saw the influx of sizeable groups of foreign immigrants over the years - people from the Netherlands from the middle ages to the beginning of the Eighty Years' War, later Portuguese Jews, French Huguenots etc. etc. There has been Englishmen living in Hamburg since Elizabethan times (the street Englische Planke near St. Michaelis commemorates their original settlement) and for a long time Hamburg was jokingly called "the most English town on the continent". Currently Hamburg is home to large Chinese and Japanese communities and a neighborhood near the harbour has fairly recently acquired the name "Little Portugal".
German films produced in Hamburg often tend to be more or less about Hamburg and/or showcase the city the best they can (see below).
The late medieval Störtebekerlied celebrates the defeat of the pirate leader Klaus Störtebeker by the seamen of Hamburg.
Hamburg crops up a bit in the works of Heinrich Heine, most notably in Deutschland, ein Wintermärchen, which describes a journey through northwestern Germany (starting in Aachen on the western border) to Hamburg not long after more than a third of the inner city was destroyed in the Great Fire of 1842 and which ends with a tête-à-tête between the author and Hammonia, the female personification of the city. Heine lived in Hamburg for a time in his youth near his rich uncle, the banker and philanthropist Salomon Heine (who later also financially supported his nephew). Because Hamburg had a more lenient censorship than most other German states of the era, this was where most of Heine's works were published during his lifetime.
The prolific Georg Philipp Telemann (1681-1767) became director of Hamburg's church music in 1721 and spent the rest of his life there. For a time he also doubled as director of the city's opera house. A number of his works were written for civic occasion, and among his suites there are Hamburger Ebb' und Flut (Hamburg Ebb and Flow, TWV 55:C3) and the delightful Alster-Ouverture (TWV 55:F11).
There are a number of popular songs that celebrate or favourably mention Hamburg, including
Stadt Hamburg in der Elbe Auen (City of Hamburg in the Vale of the Elbe), the state anthem.
Auf der Reeperbahn nachts um Halb Eins (On the Reeperbahn Half Past Midnight)
Nimm' mich mit, Kapitän, auf die Reise (Take Me With You, Captain, On the Voyage)
Hamburg, meine Perle (Hamburg, My Pearl), sung by the fans of the Hamburger Sportverein before every home game.
"Hamburg" by Die Lassie Singers, a really charming song whose meaning is mostly lost on this non-German troper.