The 8th Month is Cheshvan (חשון) also called Marcheshvan (מרחשון), and it is significant in that is is the only month on the Jewish calendar that has no holidays, other than Shabbat.
There are two annual events in Chesvhan:
7 Heshvan - V'tein Tal u-Matar ("Deliver Dew and Rain"), a prayer, is added to the Shemoneh Esrei prayers in Israel. If no rain has fallen by the 17th of the month, special prayers are added for rain
Bahab - According to most customs, on the first Sabbath of Cheshvan, a prayer is recited on behalf of all those who are going to fast on Bahab. Bahab, or in Hebrew בהב stands for 2, 5, 2, which means Monday, Thursday and Monday. On the Monday, Thursday and second Monday after the Sabbath, the custom is to fast and/or recite penitential prayers called Selichot. According to the Ashkenazi custom, the second Monday of Bahab is the Monday before Rosh Chodesh Kislev, the Thursday is the Thursday preceding that, the first Monday is the Monday preceding that and the Sabbath, in which the prayer is recited is the Sabbath preceding that. Bahab is also observed at the beginning of Iyar.