Day trips from Munich?

Kit,

Are you driving? Dachau Concentration Camp would be the closest and the King Ludwig trifecta of  Linderhof Palace, Neuschwanstein Castle and Hohenschwangau are also great options. If you're heading south, the Pilgrimage Church of Wies is beautiful to see. If you're looking for views of the alps, head south to the Zugspitze or the The Eagle's Nest on a clear day.

If you're into cars, the Audi Museum is not far to the north or you can head to Stuttgart for the Mercedes-Benz Museum or Porsche Museum. Rothenburg Ob der Tauber is one of my favorite German cities and less than a 3 hour drive-definitely a popular spot for daytrippers. 

Munich is in one of the nicest parts of Germany: Bavaria. The countryside surrounding Munich is very picturesque. To the west is the Black Forest Will you be driving? If not I suggest taking a train to Friedrichshafen Bodensee and crossing Lake Constance to the capital of the lake: Konstanz which is on the Swiss border. The lake is really beautiful and there are lots of lovely little towns to see, like Lindau and MeersburgKonstanz

You've got some great answers already! In addition, I would add Bamberg.  It's Germany's largest UNESCO World Heritage Site and looks like something straight out of a story book!

We did Dachau Concentration Camp and Fussen/Neuschwanstein Castle which were great! You could even do Nuremberg if you wanted. If you're travelling by train it's a good deal because you can get a Bayern pass for only 26 Euro which gets you all day travel around Bavaria!