German-speaking countries used many different calendars. Before 1582, all records in Europe used the Julian calendar, a solar-based calendar. The Gregorian calendar, differing in the treatment of leap years, was created in 1582 to bring the calendar closer to the solar calendar. In German speaking countries, Catholics began using the new pope-created calendar immediately, whereas the the Protestants continued to use the Julian calendar, only making the change on irregular, later dates (see the resources below).
German Date-related resources:
The book Genealogical Dates: A User-Friendly Guide by Kenneth L. Smith gives a very in depth explanation of the different calendars German researchers may encounter in Germany as well as help the researcher determine which calendar they are looking at. Smith also gives a list of conversion dates to the Gregorian calendar of each region of German speaking countries. It is available at the Family History Library in Salt Lake City, or available to purchase online.
All Catholic and some Lutheran German congregations continued to celebrate Catholic Feast days after the Reformation. This site provides this list of German Feast Days. When reading German Catholic records, it is very common to see German and Latin writing mixed, as the priest would write the names (and sometimes places and dates) in Latin and less important information in Kurrent (as seen in this example).
French Republican Calendar
Another non-German calendar system that you may possibly encounter is the French Republican Calendar, which was instituted near the end of the eighteenth century and adopted in many parts of Europe, including parts of Germany that was under French control. This calendar completely changed the organization and names of days and months and started at the year "1." It was created to do away with all traces of the "old" regime in France. The Republican Calendar ultimately proved unpopular, and even the French discontinued using it in the early years of the nineteenth century. The French Republican Calendar was based on lunar months. Sometimes the dates are also shown in the regular Gregorian calendar as well, but it may be necessary for you to do the conversion yourself.