Wochenmarkt
The weekly Wochenmarkt is on Tuesday, Thursday, and Saturday mornings; look for signs into the square from Kurze Str. or Lange-Geismar-Str. It's the best place in town to buy local produce from Göttingen and the surrounding region. Addendum, July 2008: Perhaps this should say "the second-best place", as today there is a health food store within the old town walls (and a second outlet just a few blocks to the east that sells organically grown produce - and a lot of what you find there is gown by the people who run the store, and may have been picked that same morning. Boyer's Heath Food Store Bioladen, Burg Strasse, between Friedrich Strasse and Theater Strasse. --> Added by a satisfied customer.)
Christmas markets
In December there are two Christmas markets (http://www.weihnachtsmark...), one small one outside the train station and the other sprawling from the Marktplatz area to behind the old town hall and St. John's Church. You can buy a variety of traditional German gifts, mulled wine Glühwein, and German foods.