13 Teves - Rav Moshe ben R' Dovid of Lelov (1850) was the first Chassidishe Rebbe to settle in Yerushalyim. Previously they had settled in Tzfas. The Rizhiner told him that although many great tzadikim moved to Eretz Yisroel previously, their dynasties didn't survive, but Lelov would last till Moshiach comes. R' Moshe said that if he could make it to the Kosel Hamaravi then Moshiach would come. Unfortunately, he never made it there and passed away shortly after his arrival in Eretz Yisroel. He was the son-in-law of the Yid HaKodosh. The Lelover and Bostoner Rebbes are his descendants.
13 Teves - Rav Yitzchak ben R' Asher Anshel Hakohen Huberman, the tzaddik of
13 Teves - Rav Yechiel Mordechai Gordon, Rosh Yeshivas Lomza (1965)
13 Teves - R' Shraga Feivush ben R' Boruch Hager of Zelishitshick (1936)
13 Teves - R' Menachem Mendel ben R' Yisroel Hager of Vishiveh (1941) Rosh
Yeshiva of Vizhnitz
13 Teves - R' Tzvi Hersh (Shmelkes) of Ostroh (1789) ben R' Shmuel, talmid of the Baal Shem Tov. He was considered the greatest chosid in Ostrah, was a great mekubal and is the subject of many miraculous stories
14 Teves - R' Alter Elazar Menachem ben R' Moshe Mordechai Biderman of Lelov (2001) Beloved tzadik from Bnei Brak.
14 Teves - R' Reuven Dov Dessler (1935) father of R' Eliyahu Dessler
14 Teves - R' Tzvi Hirsh of Teplik (1928), Breslover Tzadik
14 Teves - R' Mordechai Twersky of Lavoi (1905)
14 Teves - R' Aryeh Moshe Eliyahu ben R' Shmuel Kaplan (1983) author of many seforim and translater of Meam Loez
15 Teves - Mesharshia bar Pakud, Amora
15 Teves - Rav Huna, Amora
15 Teves - Mari bar Mar Zutra, Amora
15 Teves - R' Chaim Mordechai ben R' Itamar Rosenbaum of Nadvorna (1978)
15 Teves - R' Noson Nota Natkin ben R' Asher (1887) was a grandson of the Shaagas Aryeh and son-in-law of R' Yosef Zundel of Salant. Although he lived most of his life in Yerushalayim, he is buried in NY at Union Field Cemetery, (near Rabbi Jacob Joseph) because he died while collecting money for the Yishuv in Eretz Yisroel.
15 Teves - R' Refoel of Barshad (1827) ben R' Yaakov Yukel was from the greatest talmidim of R' Pinchas Koritzer. The website Two Tzaddiks has lots of information on them.