Depending on the denomination of Judaism, the terms for a modern Jewish place of worship are synagogue, shul and temple. These words' usage bears the closest resemblance to the Christian "church" or Islamic "mosque." The most common term used outside of Jewish circles is synagogue.
"Synagogue" is derived from a Greek translation of the Hebrew phrase meaning "place of assembly." The term "temple" is primarily used by the Reformed Jewish sect, but is considered problematic for Conservative and Orthodox Jews. These two groups only use "temple" to describe the historic structure in Jerusalem that was destroyed in A.D. 70. "Shul" more appropriately translates as school, but this term is less commonly used.