Over at James Reasoner's blog where he was reviewing Sergio Leone's mob film Once Upon a Time in America, I mentioned the film being based on a paperback original. I didn't remember the book's title, but I looked it up just now (while doing something completely different). It's Harry Grey's The Hoods. The book was published by Signet in 1955, and it seems to be in print from BlackMask.com (as a POD book, and I've heard these are riddled with typos and printing errors).
Here's what an Abebooks seller has to say:
"Generally described as a novel in secondary sources, yet (in this edition at least) definitely given a non-fictional sheen by the cover matter: "one of the most amazingly frank exposures of gangster life ever written" is the front cover tagline, and the author is described as "an ex-Hood himself" by Mickey Spillane in his back-cover blurb. The book is narrated by "Noodles," the character played by Robert De Niro in the 1984 Sergio Leone film version ONCE UPON A TIME IN AMERICA, and tells the story of a group of Jewish gangsters from their boyhood-chum days through their rise to prominence in the organized crime milieu of New York's Lower East Side."
There's an earlier film based on another book of Grey's, called Portrait of a Mobster (1958). The film was directed by Joseph Pevney and scripted by Howard Browne.
Edit: Thanks to Tapani Bagge, who noticed my error on the Pevney film. It's now corrected.