1 Elul – R' Dovid HaNagid (1300) ben R' Avrohom ben Rambam
1 Elul – R' Chanoch Henoch Dov of Alesk ben R' Shmuel (1884), the Lev Sameach, was a son-in-law of the Sar Sholom of Belz in his first marriage and in his second marriage was a son-in-law of R' Meir ben R' Levi Yitzchok of Berditchev
2 Elul – R' Yitzchak Bar Sheshes, the Rivash (1408)
2 Elul - R' Avraham Yaakov Friedman of Boyan-Lvov HY"D (1942) ben R' Yitzchok, author of Nachalas Yaakov, murdered by the Nazis y's.
2 Elul – R' Eliezer ben R' Yisroel Hager, the Damesek Eliezer of Vizhnitz (1946) He is buried on Har Hazeisim.
2 Elul – R' Shmuel Dovid Walkin (1979) was Rov in Shanghai during WWII and later in Queens, NY. He was the son of the Pinsker Rov, the Bais Aharon.
3 Elul - R' Yissochor Bertcha Leifer of Nadvorna (1848) ben R' Yitzchok of Kalish was a great-grandson of R' Meir "HaGadol" of Premishlan
3 Elul - R' Yitzchok Yeshaya Halberstam HY"D of Tchechoiv (1943) was the youngest son of R' Chaim of Sanz
3 Elul - R' Moshe Friedman HY"D of Boyan-Krakow (1943) ben R' Sholom Yosef
3 Elul - R' Shraga Feivel Mendlowitz was the legendary head of Yeshiva Torah Vodaas and founder of Torah Umesorah. He used to ask to be called Mister Mendlowitz, to which one of the great tzadikim said, his name is "Nister" Mendlowitz
3 Elul – R' Avrohom Yitzchok HaKohen Kook (1935)
3 Elul – R' Sholom Eichenstein of Zidichov-Tsfas (1988) ben R' Asher Yeshaya
4 Elul - R' Meir Simcha Hakohen of Dvinsk (1926) ben R' Shimshon Klonomus, author of Ohr Someach and Meshech Chochma
4 Elul - R' Aryeh Leib Tumim, author of Gur Aryeh
4 Elul – R' Eliyahu Kramer, grandfather of the Vilna Gaon
5 Elul - R' Dovid Tzvi Shlomo (1918) ben R' Elazar Menachem Mendel Biderman of Lelov, one of the great tzadikim of Yerushalaim, buried on Har Hazeisim
5 Elul - R' Moshe Ahron ben R' Chaim Pinto, great tzadik who lived in Ashdod
6 Elul - R' Yom Tov Lipman Heller (1654), author of Tosfos Yom Tov
6 Elul - R' Yekusiel Yehuda Teitelbaum of Sighet (1883) ben R' Elazar Nisan, author of Yetev Lev, Yetev Ponim, Avnei Tzedek and Rav Tov L'Beis Yisroel. He was a grandson of the Yismach Moshe and grandfather of the Satmar Rebbe
6 Elul - R' Moshe Mintz, author of Shailos U'Tshuvos Maharam Mintz
6 Elul - R' Yechezkel Sarna (1969), Rosh Yeshiva of Chevron, great tzadik and talmid of the Chofetz Chaim and Slabodka
6 Elul - R' Meir Zvi Ehrentreu, Manchester Yeshiva Rosh Kollel and RoshYeshiva
7 Elul - R' Reuven Margolios, author of Margolios Hayom and many otherseforim
7 Elul – R' Eliyahu (1859), father of the Ben Ish Chai
7 Elul - R' Aryeh Leib Lopian, Rosh Yeshivas Gateshead
8 Elul – R' Shlomo ben R' Yosef Karo (1889) was Rov in Saana, Yemen
8 Elul - R' Michoel Ashkenazi (1889) was a Rov in Aram Soba, Syria
9 Elul - Dan ben Yaakov Avinu (also birthday)
9 Elul - R' Tzadok ben R' Yaakov HaKohen Rabinowitz of Lublin (1900), author of Pri Tzaddik, Tzidkas HaTzadik and numerous other seforim.
9 Elul - R' Nachum Mordechai ben R' Alter Yisroel Shimon Perlow of Novominsk (1976) was a descendant, ben acher ben, from R' Mordechai of Neshchiz. His son, R' Yaakov is the current Novominsker Rebbe.
9 Elul - R' Yonoson Shteif (1958), Viener Rov and renown posek
10 Elul - R' Pinchos of Koritz (1790) ben R' Avrohom Abba Shapiro, a descendant of R' Noson Nota Shapiro, the Megaleh Amukos. He was not only one of the greatest talmidim of the Baal Shem Tov, but was also considered a friend of the Baal Shem Tov. His teachings are collected in Medrash Pinchos, Nofes Tzufim and Imrei Pinchas. His talmidim included R' Raphael "der Emesser" of Bershad and the Shpoler Zeide. See here for more. There is a site dedicated to R’ Pinchas and R’ Raphael, Two Tzaddiks.
10 Elul - R' Yitzchok of Bohush (1896) ben R' Sholom Yosef of Sadiger
10 Elul - R' Moshe Yehudah Leib of Pashkan (1947) ben R' Yitzchok of Bohush, author of Birchas Moshe.
11 Elul - R' Sholom Yosef Friedman of Sadiger (1851) oldest son of R' Yisroel of Ruzhin
11 Elul - R' Avrohom Yaakov Friedman of Sadiger (1883) second son of R' Yisroel of Ruzhin
12 Elul - R' Shimon of Toledo, son of the Rosh (1342)
12 Elul - R' Simcha Bunim of P'shischa (1827) ben R' Tzvi, talmid of the Chozeh and the Yid HaKodosh
12 Elul R' Moshe Elyokim Briah Hopstein of Koznitz (1828), son of the Kozhnitzer Magid, R' Yisroel
12 Elul - R' Yitzchak Zelasnik, Rosh Yeshiva of Me'or Eliyahu
12 Elul - R' Menachem Menashe (1968) was a great tzadik from Turkey. He wrote Ahavas Chaim, a sefer filled with halacha, mussar and more, including fascinating stories of tzadikim, including many Chassidish Rebbes. You can read about him here, about halfway through the article.
13 Elul - R' Yosef Chaim of Baghdad (1909) ben Eliyahu, author of Ben Ish Chai and many other seforim
13 Elul - R' Yaakov Yisroel Twerski of Cherkas (1876) ben R' Mordechai of Chernobyl
13 Elul - R' Avrohom Yisochor Ber HaKohen Rabinowitz of Radomsk (1892), wrote Chesed L'Avrohom. He was son of the Tiferes Shlomo, R' Shlomo of Radomsk
14 Elul - R' Yosef Yuska (1867) ben R' Yisroel Ashkenazi, author of Ohel Yosef
15 Elul - R' Moshe Alshakar, author of Shailos U'Tshuvos Maharam Alshakar and "Kol Bruei Malah U'matah", a piyut of praises to Hashem, featured at the beginning of some siddurim.
15 Elul - R' Chanoch Eiges of Vilna (1941), author of Marcheshes
15 Elul - R' Yaakov Koppel Chassid (1787) ben R' Nechemia Feivel, was the Shliach Tzibur of the Baal Shem Tov and forefather of the Kosov-Vizhnitz dynasty. He was a descendant of R' Ovadia of Bartenura.
16 Elul - R' Yitzchok HaKohen Shapiro (1582) father-in-law of Maharam Lublin
16 Elul - R' Avrohom Avigdor Nochum of Strikov (2001) ben R' Yaakov Yitzchok Dan Landau was a talmid of the Brisker Rav and became Rebbe of Strikov after WW II, first in Tel Aviv and then Bnei Brak.
16 Elul - R' Yechi Shnior (1994), talmid of Baba Sali
17 Elul - R' Chaim Benveniste (1673), Rav in Izmir and author of Knesses Hagedola
17 Elul - R' Yaakov Koppel Reich (1900), Av Beis Din of Budapest
18 Elul - R' Yehuda ben Betzalel Loew, the Maharal of Prague. See Heichal HaNegina: The Patience of the Maharal
18 Elul - R' Abdullah Somech, Rebbe of the Ben Ish Chai and head of Iraqi Jewry
19 Elul - Rabeinu Yaakov of Orleans HY"D (1189), a talmid of Rabeinu Tam, he was killed in London at the coronation of Richard the Lion-hearted
19 Elul – R’ Moshe of Orzistchov ben R’ Pinchas of Ostroh. After being orphaned, he was raised by the Shpola Zaide.
19 Elul - R' Hillel Vitkind, Rosh Yeshiva of Beis Hillel in Bnei Brak
19 Elul - R' Moshe Tzvi Aryeh Bick (1990) great posek, his father, ben R' Chaim Yechiel Michel was the last Rov of Mezibuz. Their family had been the heads of the Bais Din in Mezibuz for seven generations, since the days of the Baal Shem Tov. He is buried in Beth David Cemetery on Long Island.
20 Elul - R' Yosef Shlomo Kahaneman, R' of Ponevezh, Lithuania, and founder of the Ponevezh Yeshiva in Bnei Brak (1969)
20 Elul - R' Avrohom ben R' Naftali Hertz Sternhartz (1955), great-grandson of R' Noson of Breslov, he was the leader of Breslov in his time He was known as the Kochov Lev.
20 Elul - R' Eliyahu Lopian (1970), author of Lev Eliyahu, and legendary mashgiach in Kelm and Kfar Chassidim
20 Elul - R' Moshe Aryeh Freund (1996), Av Beis Din of Eida Hachareidis in Yerushalayim
21 Elul - R' Yonoson ben R' Noson Nota Eibeschitz (1764), Rov of Altona, Hamburg and Metz, and author of Kereisi U'Pleisi, Urim VeTumim, and Yaaros Devash
22 Elul - Rabeinu Yaakov ben R' Moshe HaLevi Segal Moellin of Mainz (1427), the Maharil, the primary source of Minhagei Ashkenaz
22 Elul - R' Mordechai Dov Twerski of Hornesteipel ben R' Meshulam Zusia Ytzchok. He was a descendant, ben avcher ben, from the Rebbe, Reb Zusia of Anipoli. He was raised by his maternal grandfather, the Cherkasser Rebbe after his father died, so he adopted the family name, Twerski.
23 Elul – R’ Yisroel of Pikov (1818) ben R’ Levi Yitzchok of Berditchev
23 Elul - R' Uri "the Seraph" of Strelisk (1826) ben R' Pinchos, his main Rebbe was R' Shlomo of Karlin
23 Elul - R' Meir Yehuda Getz, R' of the Kosel and Rosh Yeshivas Beit El (1995)
23 Elul - R' Yitzchak Menachem Mendel Danziger (1942), the Alexander Rebbe, killed in Treblinka with eight of his children HY"D, he was the son of R' Shmuel Tzvi of Alexander
24 Elul - Chabakuk Hanavi (c. 480 B.C.E.)
24 Elul - R' Yisroel Meir ben R' Aryeh Zev HaKohen Kagan (1933), the Chofetz Chaim
24 Elul - R' Yechezkel Abramsky (1976), Rov of Slutsk and London, author of Chazon Yechezkel
25 Elul - R' Elazar (102 C.E) ben R' Shimon bar Yochai
25 Elul - R' Yechiel Michel (1786) ben R' Yitzchok, the Maggid of Zlotchov, talmid of the Baal Shem Tov
25 Elul - R' Aharon (1901) ben R Yaakov Abuchatzera
26 Elul – R’ Elyakim Getz of Ostroh (1824) ben Reb Yaakov Yosef ( Reb Yeivei) He printed the seforim of his illustrious father. Was known for his devotion to providing for the destitute.
27 Elul - R' Noson Adler, Rebbe of the Chasam Sofer
27 Elul - R' Sholom ben R' Elazar Rokeach (1855), the first Belzer Rebbe, known as the Sar Sholom
28 Elul - Shaul Hamelech and his three sons died in Gilboa 4 months after Shmuel Hanavi's death (878 B.C.E)
28 Elul - R' Chaim Yehuda Leib ben R' Avrohom Dov Auerbach (1954), Rosh Yeshiva Sha'ar Hashomayim, father of R' Shlomo Zalman
29 Elul - R' Yaakov Halevi Lipschutz, secretary of Rav Yitzchok Elchonon Spector and author of Zichron Yaakov