“Forget the movie, let’s pull the job!”

That, legend has it, is what Frank Sinatra joked upon hearing the plot for Ocean’s 11, the 1960 Vegas heist flick that went on to become the Rat Pack’s signature big-screen adventure.

It’s no wonder Sinatra and his kindred crew of high-living, hard-drinking, skirt-chasing buddies — Dean Martin and Sammy Davis Jr., especially — were gassed to make such a movie: just like their characters, they loved a good caper. From the late ’50s until they began to splinter apart in the mid-’60s, they were showbiz’s unrivaled kings of swing, quick-with-a-quip cats who could swagger into any joint — from the Sands to Sardi’s — and make it the most.

[Buy the LIFE book, The Rat Pack: The Original Bad Boys.]

LIFE magazine’s photographers, of course, trailed the Pack through those magic years, coming away with priceless material for some of the best celebrity photo-essays the magazine ever ran. But of the thousands of shots taken, many were never published — until now. Here, in celebration of sharkskin sits, Scotch on the rocks, smoky rooms and fedoras tilted just so, LIFE presents a slew of previously unpublished photos of the Rat Pack, together and apart, during their heyday.