It is not unusual for a synagogue to be without a rabbi, at least temporarily. However, the rabbi is a valuable member of the community, providing leadership, guidance and education. Synagogues do not pass around collection plates during services, as many churches do. This is largely because Jews are not permitted to carry money on holidays and shabbat . It is important to note, however, that you do not have to be a member of a synagogue in order to worship there.
Synagogues are, for the most part, independent community organizations.
In the United States, at least, individual synagogues do not answer to any central authority. There are central organizations for the various movements of Judaism, and synagogues are often affiliated with these organizations, but these organizations have no real power over individual synagogues. The portion of the synagogue where prayer services are performed is commonly called the sanctuary. Synagogues in the United States are generally designed so that the front of the sanctuary is on the side towards Jerusalem, which is the direction that we are supposed to face when reciting certain prayers. Probably the most important feature of the sanctuary is the Ark.