When going to a traditional Viennese Kaffeehaus, people don't simply order "a coffee". This would immediately be followed by the waiter's question: "Was für einen Kaffee hätten Sie denn gerne?" (What kind of coffee would you like?)
Since some establishments can serve up to 40 kinds of coffee, it is easy to get lost in the jungle of terms and expressions. Here is a list of the most common options to help you choose. Order a "classic", or go for the unknown if you feel adventurous!

The most popular coffees are:

Melange - 50% espresso and 50% hot milk, the popular Melange is served with milk foam on top (like an Italian "cappuccino").

Brauner - Black coffee with a dash of milk. It comes as "Großer Brauner" (big) and "Kleiner Brauner" (small).

Verlängerter Brauner - Watered-down version of the "Brauner".

Mocca or Schwarzer - Coffee without milk. It comes as "Großer Schwarzer" (big) and "Kleiner Schwarzer" (small).

Verlängerter Schwarzer - Like the "Schwarzer", but with a little bit more water in it.

Cappuccino - Unlike its Italian version, Viennese cappuccino has whipped cream on top. If you want an Italian cappuccino, you should order a "Melange".

Kaffee verkehrt or Milchkaffee - Coffee with a lot of milk.

And the more exotic names:

Biedermeier Kaffee - Big "Mocca" with apricot liquor and whipped cream.

Einspänner - Black coffee or "Mocca" served in a glass topped with whipped cream.

Fiaker - A "Fiaker" is a carriage pulled by horses that takes tourists around the town. In a Kaffeehaus, however, it is an espresso with rum or cognac served in a glass topped with whipped cream.

Franziskaner - "Melange" with whipped cream.

Kaisermelange - "Mocca" mixed with an egg yolk and honey or sugar.

Kapuziner - Big "Mocca" with a dash of milk or whipped cream. It looks as brown as the dress of a "Kapuziner" (Capuchin) monk, hence the name.

Maria Theresia - "Mocca" with orange liquor.

Mariloman - Hot "Mocca" with Cognac.

Mazagran - Cold coffee with rum and ice.

Mozart Kaffee - Big "Mocca" with cherry Brandy and whipped cream.

Obermayer - Big "Mocca" topped with a bit of cold cream.

Phasisäer - Black coffee topped with whipped cream and served with a glass of rum.

Türkischer Kaffee - Turkish coffee -- very strong black coffee served with grounds in a copper pot.

Wiener Eiskaffee - Cold "Mocca" with vanilla ice-cream and whipped cream -- more a dessert than a drink!