Holiday Grind by Cleo Coyle (mostly about Christmas but Hanukah is mentioned)
Beautiful Lie the Dead by Barbara Fradkin
Festival of Deaths by Jane Haddam
Out of the Frying Pan into the Choir by Sharon Kahn
Saturday the Rabbi Went Hungry by Harry Kemelman
Murder at the Minyan by Shlumat E. Kustanowitz
The Body in the Sleigh by Katherine Hall Page (mostly about Christmas but Hanukah is mentioned)
Chanukah Guilt by Ilene Schneider
The Tattooed Rabbi by Marvin J. Wolf
Children's Hanukah Mysteries
Rabbi Rocketpower and the Mystery of the Missing Menorahs - A
Hanukkah Humdinger! by Rabbi Susan Abramson and Aaron Dvorkin and Ariel DiOrio
Mystery Short Stories
"Mom Lights a Candle" by James Yaffe, appeared in Mystery: The Best of 2002, ed. by Jon L. Breen.
"Hanukah" by Morris Hershman in Cat Crimes for the Holidays, ed. by Martin Greenberg, Edward Gorman and Larry Segriff
"The Worse Noel" by Barb Goffman in The Gift of Murder.
"Death on the List" by B.K. Stevens (AHMM, January 1999)
For more info on Jewish short story mysteries, check out Steven Steinbock who blogs on Criminal Brief, the Mystery Short Story Web Log Project.
"Navidad" by Elizabeth Zelvin, EQMM, January 2011
"No Candles for Antiochus" by Barry Ergang
Children's software mystery game: Who Stole Hanukkah? offered in five languages: English, Hebrew, Russian, French and Spanish
Other Games for Children: The Case of the Stolen Menorah: An Enlightening Hanukkah Mystery