I'll be in Munich from December 24 to December 28 (early morning). Since Germany really shuts down over Christmas, does anyone have any suggestions for things to do that will be open over that period?

The Christmas market (in and near the Marienplatz) will still be operating on the 24th from 10 AM to 2 PM and is well worth a visit. Things will be largely back to normal on the 27th and 28th. For the 25th and 26th, the best recommendation I can give is to visit churches. If that appeals to you, the Frauenkirche (near the Marienplatz), the Asamkirche (on the Sendlingerstr.), and the cathedral in Freising (about 25 miles north, the last station on the S-1 line) are all quite attractive.

According to the posted schedules:

I just checked a few of the major museums

The Deutsches Museum is open on the 26th
The Bavarian National museum is OPEN from 10-5 on both the 25th and 26th
Both the Neue and Alte Pinakothek are closed on the 25th, but open the 26th
The Residenz in also closed on the 25th but open the 26th.

This is very similar to what we found last year at Easter - at least one major museum was open each day. I believe it was again the Bavarian National Museum that was open on Easter, and they were very busy.

You think Germany shuts down over Christmas??!! You've obviously never spent Christmas in the UK... which really DOES shut down for Christmas. No public transport on Christmas Day, and hardly any on Boxing Day.

Shops are shut over Christmas in Germany, like they are on all Sundays and public holidays. That's something you very much have to expect in a lot of European countries. Some other attractions will be open on Christmas Day and/or Boxing Day, as others have mentioned. Christmas Eve afternoon/evening is the closest Germany comes to shutting down, as that's when everybody is at home with their families.

If the weather is nice (and I haven't checked the forecast) why not jump on a train and take a trip out into the countryside on Christmas Day or Boxing Day?