Jewish mobsters predominated the booze rackets in most cities during Prohibition. They caught a break from Al Capone, who was such a publicity hound that most Americans believed (and still believe) that Italians predominated the booze trades. Jewish gangsters also built Las Vegas--though Bugsy Siegel gets most of the credit, the real builders were Moe Dalitz and Meyer Lansky.

As for the Russian and Israeli "Mafia": It's not clear how many of them were or are Jewish, for an interesting reason:

All citizens of the former Soviet Union were required to carry internal passports that, among other things, identified their republic of national origin (i.e., Ukraine, Azerbaijan, Georgia, etc.). But Jews had to carry passports stamped with "Jew." It was a reflection of Stalin's anti-Semitism--he called Jews "rootless cosmopolitans"--that carried forward into the Seventies.

The US Congress passed the Jackson-Vanik Act in 1974, which gave the USSR favorable trading status with the US in return for allowing Soviet Jews to immigrate to Israel or the US. All of a sudden, a tremendous black market emerged for counterfeit Jewish internal passports. Since gangsters dominated the counterfeiting rackets, they gave themselves phony Jewish passports. So, a great many non-Jewish gangsters palmed themselves off as Jews to get to Israel and America and establish new rackets.

The example I like most is of Marat Balagula, who was identified as the number-one "Jewish Russian Mafioso" in America by law enforcement. "Marat" is not a traditional Jewish surname. "Balagula" comes from the Hebrew b'aal agula, "master of the wheel," meaning a carter--a respectable trade in Biblical times. But in modern Yiddish slang, a "balagula" is an uncouth person--a thug or gangster. Whatever his real name, Marat fashioned a phony passport for himself and gave himself a last name that (like a secret password) proudly proclaimed him as a gangster.