Come in …

"A whole generation was cheated of radio drama. Only here in America did Madison Avenue say, 'This is it. Without a picture there ain't no story.' Nonsense! The finest stories are right in your head," Himan Brown told Time magazine in 1981.
One thousand-ninety-nine episodes of radio veteran — he produced shows like Inner Sanctum, The Thin Man, Bulldog Drummond, Dick Tracy and Nero WolfeBrown's CBS Radio Mystery Theater were broadcast from January 6, 1974 to December 31, 1982. The episodes aired daily till season seven, with five shows a week and by the early 1980s had 3.6 million dedicated listeners.

During the 1970s other attempts at reviving the radio drama included the Rod Serling-hosted The Zero Hour from 1973 to 1974 which had five-part, half-hour shows that aired Monday through Friday; the Sears Radio Theater in 1979 (the next year known as the Mutual Radio Theater) with different hosts and themes for each day's show — western, comedy, mystery, "love and hate," and adventure; NPR's Earplay; and the Himan Brown-produced youth-oriented General Mills Radio Adventure Theater in 1977 using many of the same writers and actors from Mystery Theater but it is the Mystery Theater that lasted longer and is best remembered.
I used to listen to the Mystery Theater on Tampa's WFLA-AM (I remember not wanting to miss the fifth and final episode of the of "Last Days of Pompei" and listening to it on the ride home home after watching the Tampa Rowdies play Nottingham Forrest in a nil-all draw) in the late '70s till the end of the show's run; another excellent show (and a story for another time) was the science fiction detective drama Dry Smoke and Whispers on community radio station WMNF and received praise from Harlan Ellison.

The announcer spoke: "The CBS Radio Mystery Theater presents," followed by eight seconds of the sound effect of a creaking door then the theme music (bonus fact: the theme was originally used in The Twilight Zone episode "Two" and can be heard at about the 4:35 mark) and "Come in … Welcome … I'm E.G. Marshall … ." Promising the "fear you can hear," Marshall acted as the listener's guide to the world of "terrifying imagination" on the other side of that creaking door except for the last season when Tammy Grimes became host.

The first episode "The Old Ones are Hard to Kill" starred Agnes Moorehead (Suspense "Sorry Wrong Number") and aired a few months before her death (she also appeared in the episode "Ring of Truth").
The copy of the episode I've linked to was from WDAF-AM in Kansas City and has the original ABC news, commercials and PSAs.
Mystery Theater is available from several OTR websites and podcasts online for listening or downloading. Himan Brown is still alive and is still the rightsholder of the series so if you find any collections of the show for sale it is without his approval.
The episodes vary in quality — some have the commercials, station IDs and news edited out and some are the versions that NPR aired in 1998 with Brown as announcer.

Early reviews were not so kind. From the New York Times: "Mention radio drama to those who reached adolescence before the early fifties and they are likely to go limp and soggy with nostalgia. Listen to the new "CBS Radio Mystery Theater" series, and the nostalgia itself goes limp and soggy."and Chicago Tribune: "If CBS Radio Mystery Theater doesn't get better in a big hurry, radio drama will be buried in a grave from which resurrection may be forever impossible." Early into the second season (that year the show received a Peabody Award) James Brown of the Los Angeles Times noted that "The second year of CBS Radio Mystery Theater began last Monday on KNX, and those prophets of doom of last year, convinced that Himan Brown's nightly broadcasts of original radio drama were a foregone flop, have now retreated quietly."