I should add:
Light One Candle
Go Down, Moses
Little Moses
Joshua Fit De Battle Of Jericho
Down By The Riverside (sans the references to Jesus)
By The Waters Of Babylon
Man Come Into Egypt
Dayenu
L'Chaim
Otchee Tchornya
Kaleenka
 

and other non-Jewish songs such as:
Bèsame Mucho
Que Sera Sera
Always
Anniversary Song
Sentimental Journey
Blue Skies
Edelweiss
Du Liegst Mir Im Herzen
Beer Barrel Polka
God Bless America
America The Beautiful
Lara's Theme
Let Me Call You Sweetheart

and Allan Sherman parodies such as:
Camp Granada
Harvey And Sheila