Access. It’s a big word in the media these days, when celebrity culture is the engine driving so much online content and so much offline conversation. Who has access to Celeb A? How did that magazine get access to Celeb B? Where on earth did that gossip site get those tawdry (and hypnotic) photographs of Celeb C?

In its prime, LIFE magazine — almost alone among all of the popular culture publications of its day — enjoyed the sort of access to A-list stars (and, admittedly, to lesser lights) that today’s tabloids and paparazzi can only dream about.

Here, a fond look back at some of the 20th century’s biggest, brightest entertainers, in the friendly confines of their own homes.