What Jewish festivals are celebrated in a synagogue?

Judaism has many holidays and Holy Days. Almost all of them are marked by additions to
the regular daily prayers, whether in the regular daily synagogue service or in regular daily
private prayer.

The main holy days are:

1 Rosh Hashanah - The Jewish New Year
2 Yom Kippur - Day of Atonement
3 Sukkot - Feast of Booths (or Tabernacles)
4 Pesach - Passover
5 Shavuot - Feast of Weeks - Yom HaBikurim

The holiest day on the calendar is Shabbat (The Sabbath) which occurs every Friday night at sundown to Saturday night at sundown.

This is a list of most of the major holidays and minor festivals:
1 Rosh Hashanah - The Jewish New Year
2 Aseret Yemei Teshuva - Ten Days of Repentance
3 Yom Kippur - Day of Atonement
4 Sukkot - Feast of Booths (or Tabernacles)
5 Shemini Atzeret and Simchat Torah
6 Hanukkah - Festival of Lights
7 Tenth of Tevet
8 Tu Bishvat - New Year of the Trees
9 Purim - Festival of Lots
10 Pesach - Passover
11 Sefirah - Counting of the Omer
12 Lag Ba'omer
13 Shavuot - Feast of Weeks - Yom HaBikurim
14 Seventeenth of Tammuz
15 The Three Weeks and the Nine Days
16 Tisha B'av - Ninth of Av
17 Rosh Chodesh - the New Month
18 Shabbat - The Sabbath - שבת
19 Yom HaShoah - Holocaust Remembrance day
20 Yom Hazikaron - Memorial Day
21 Yom Ha'atzmaut - Israel Independence Day
22 Yom Yerushalaim - Jerusalem Day