Whether or not the term "Jew" is offensive often depends on subtle shades of meaning. "I know it when I see it" is, unfortunately, how it usually works. My rules are:
1) "Jews," as a plural is usually ok, although when preceded by "the," it's often better to substitute the term "Jewish people". Example: "The Jews are often worried about the survival of Israel" could be offensive. However, "Jews are often worried about the survival of Israel" or "Jewish people are often worried about the survival of Israel" are both ok, although the latter may be a bit better than the former.
2) The term "A Jew" is often offensive, but not always. Example: "He's a Jew" is usually better avoided. "He's Jewish" is better. "He's a Jewish person" is totally unnecessary, and sounds like someone is terrified of being offensive. Here's where I wouldn't find "a Jew" offensive, depending on the punchline: "A Catholic, a Protestant, and a Jew walk into a bar...." Also, to me, "Jewish" refers to religion, whereas "a Jew" refers more to ethnicity.
3) Never, EVER use "Jew" as an adjective. Example: "Jew cooking is usually heavy," should be "Jewish cooking is usually heavy."
4) If the three letters, j, e, and w appear together in other contexts, leave them alone. Example: "I'm not a fan of gold jewelry." 
Except for the last one, I've found myself explaining these amorphous "rules" for real, to well-intentioned people.
Audrey Liebross (who is proud to be a Jew, proud to be Jewish, proud to be a Jewish person -- whatever)
Audrey, the Phantom Phanatic, who nonetheless would rather be Jean Valjean, who knew how to make lemonade out of lemons.
