I know for a fact that William Shatner (Kirk) and Leonard Nimoy (Spock) from TOS are both Jewish.
Yes, Shatner is a Jewish-Canadian, and Nimoy is Jewish-American. Shatner is an Anglophone Canadian from Montreal, which has a significant Jewish-Canadian population. There is an excellent steakhouse there called "Moishe's", which serves a twenty-ounce Porterhouse ProfessorTrek 07:06, August 8, 2011 (UTC)
The question was about characters, not actors.
>>What's the point of answering a question until and unless there's a consensus as to semantics? Each answer should be prefaced by a definitional cross-references section. "characters in Star Trek" vs "Star Trek characters" - which one is the broader definition?
Earth religion was not really dealt with that much in Star Trek. Gene Roddenberry believed we would have grown past it by the 23rd Century.
Star Trek: The Next Generation Companion suggested that the Rozhenkos (Worf's adoptive parents) are Jewish. There were also some background characters identified as such.
You are right that no characters are explicitly Jewish, although some Jewish ancestry is implied.
In terms of Jewish actors, there are too many to list them all, but to offer some:
William Shatner, Leonard Nimoy, Walter Koenig, Brent Spiner, Armin Shimmerman, Max Grodenchik, Aron Eisenberg, Wallace Shawn.