Observant Jewish men wear a hat almost all the time.
The most common hat for men in the synagogue is a small round cap called a yarmulke (Yiddish) or a kippah (Hebrew), but an ordinary homburg or street hat will be accepted.
Hats are always available for visitors, but a hair grip comes in handy to keep a kippah on.
Adult men (i.e. those over the age of 13) often wear a Tallit or prayer shawl for morning prayer. A Tallit has fringes (called tzitzit) on the edges to remind the wearer to observe God's commandments - as commanded by God in the Bible.