Prinz Myshkin is Munich's most well-known vegetarian restaurant and is popular with non-vegetarians, too - has a very cool atmosphere, great food, sensible prices, and best of all, the smokers have their own room, so non-smokers can enjoy their food (not always something to be taken for granted in Munich). It can be pretty busy after about 7.30pm, so if you want to go in the evening, it's a good idea to make a reservation.
www.prinzmyshkin.com/index.html
It's on Hackerstr. just off Sendlinger Str. (5 minutes walk south from Marienplatz).