Perhaps the finest Theodore Bikel CD available is from Rhino Handmade, Theodore Bikel's Treasury Of Yiddish Theatre And Folk Songs. It includes 26 tracks, taken from three Elektra Albums:

Theodore Bikel Sings Yiddish Theatre & Folk Songs, Elektra EKS-7281 (1964)
1. Chasese Tants [Wedding Dance]
2. Doina
3. Beygelach [Bagels]
4. Di Grine Kuzine [The Greenhorn Cousin]
5. Pintale [A Letter to the Rabbi]
6. Machatonim [In-Laws]
7. Shabes Shabes [Sabbath Sabbath]
8. Mayn Shtetele Belz
Theodore Bikel Sings More Jewish Folk Songs, Elektra EKS-7165 (1959)
9. Hulyet, Hulyet Kinderlech [Frolic, Play, My Little Ones]
10. Lomir Alle Zingen [Let Us All Sing]
11. Zemer [A Song for Al Grierson]
12. Fidler [A Fiddle]
13. Drei Techterlech [Three Daughters]
14. Kinder Yorn [Childhood Years]
15. Dona, Dona
16. Unter a Kleyn Beymele [Under a Little Tree]
17. Drei Yingelech [Three Little Boys]
18. Az Der Rebbe Zingt [When the Rabbi Sings]
Theodore Bikel Sings Jewish Folk Songs, Elektra EKS-7141 (1958)
19. Der Rebe Elimelech [The Rabbi Elimelech]
20. Di Younevdike Teyg [The Festival Days]
21. Kum Aher du Filozof [Come Here, My Philosopher]
22. Di Mezinke [I Gave Away My Youngest Daughter]
23. Margaritkelech [Daisies]
24. Lomir Zich Iberbeten [Let's Make Up]
25. Chazn Oyf Shabes [A Cantor Came on the Sabbath]
26. Tumbalalayka

This is a limited-quantity resissue released in 2003. I see that Amazon no longer carries it, but it should be available from some retailers.
The CD booklet is wonderful, with full lyrics and translations.

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The complete Sings Jewish Folks Songs is also available as a CD from Collectors' Choice Music:

Side 1
1. Der Rebe Elimelech
2. Di Yontevdike Teyg
3. Sha Shtil
4. Di Ban
5. Kum Aher Du Filozof
6. Di Mezinke
7. A Sudenyu
8. Achtsik Er Un Zibetsik Zi

Side 2

9. Di Mame Iz Gegangen
10. Margaritkelech
11. Mu Asapru
12. Lomir Zich Iberbeten
13. Homentashn
14. A Chazn Oyf Shabes
15. Reyzl
16. Tumbalalayka

With orchestra: Fred Hellerman, conductor.

I haven't seen this recording.