If you are interested in Culture, Museums, etc. Munich has quite a lot to offer...
The most famous ones are probably the "Alte Pinakothek", "Neue Pinakothek" and "Pinakothek der Moderne".
The "Alte Pinakothek" has famouns paintings from the "old masters" ca. 13th to 18th century. The "Neue Pinakothek" covers the rest of the 18th and the 19th century. The "Pinakothek der Moderne" focusses on modern art.
On Sunday all Pinkakotheken have a reduced admission fee of 1€. (Actually on Sunday the admission fee to all state owned Museums in bavaria is 1€).
There is a great number of art museums in Munich, if you are interested in that kind of stuff.
As mentioned before, if you are interested in technology, the "Deutsches Museum" (German Museum) is the world's largest Museum of Technology -- it is much too big to see the entirety of it on a single day.
Unlike stated above, admission is defenitely not free and the museum is not state-owned -- no reduced price on Sundays. Tours are included in the price -- some of them are (depending on the tour guide) very interesting, I recommend the one where they show their scanning electon microscope. I don't know if they offer tours in english.
The museum also has two external branch museums, one covering automobiles and one covering airplanes.
Schloss Nymphenburg (Nymphenburg Palace) built in the 15th century is a baroque palace (was the royal summer residence), which can be visited -- and it has a beautiful garden (including a botanical garden if you are interested in that kind of things).
The Residenz (royal palace) in the middle of the city also can be visited.
I think that covers the most famous cultural attractions in Munich...
Post edited May 18, 2011 by Xonea