The 8th day of Chanukah is known as "Zos Chanukah" (in earlier times it was called "Chanukas Hamiz'beach") named for the Torah portion we read. The day is mesugal for one to daven for; barren women to have children, for a Refuah Sheleimah, and for one to be blessed with increased Parnassah.
On the 8th day of Chanukah some have the minhag to say Mizmor Lesodah (tehillim 100) and Nishmas Kol Chai at night after lighting; and to make a special seudah during the day. Some Sefardim have the minhag to make a seuda for the young schoolchildren and to say Shir Hashirim with them before beginning the seudah, and to say the possuk "Shuvu Shivru Lanu Me'at Oichel" 8 times.