There are many recordings of this song, but the spelling varies:

ZOG NIT KEYNMOL, recorded by:
Emil Decameron & His Orchestra on "Tumbalalaika! [Yiddish Folksongs without Words]," 1959.
An unnamed artist on "Songs of WWII Jewish Resistance," 1989.
Sarah Gorby on "Unforgettable Songs of the Ghetto," 1989.
Lucie Skeaping & the Burning Bush on "Raisins & Almonds," 1995.
Rosalie Gerut on "We Are Here," 1996.
Jaffah Musicians & Singers Traditional on "Israeli Folk Music," 1998.
Martha Schlamme on "Sings Jewish Folk Songs," 1998.
Theodore Bikel on "Taste of Passover," 1998.
An unnamed artist on "When the Rabbi Danced: Songs of Jewish Life," 2004.
Partisans of Vilna on "Partisans of Vilna."
Paul Robeson on "Collector's Paul Robeson."

ZOG NICHT KEIN MOLL, recorded by:
Duo Peylet-Cuinot on "For the Love of Niguns, Vol. 3," 2002.

ZOG NISHT KEYN MOL, recorded by:
Daniel Kempin on "Mir Leben Eybik," 1998.

ZOG NIT KEIN'MOL, recorded by:
Chava Alberstein on "Yiddish Songs," 2000.

ZOG NIT KEYN MOL, recorded by:
Paul Zim on "Yiddish Songs of the Holocaust," 2000.

Sound samples are available for most, if not all, of these recordings at allmusic, from which I got the above information.

Most sources say: poem by Hirsh Glik (1922-1944), music by Dmitri Pokrass; some say "traditional" (incorrectly, I assume).