I've been listening to the old time radio station on Sirius lately, and have enjoyed a lot of old shows. Some favorites:

Comedies:

Burns and Allen
The Charlie McCarthy Show
Damon Runyan Theatre
Duffy's Tavern (sort of a forerunner to Cheers)
Fibber McGee and Molly
The Great Gildersleeve
Halls of Ivy
The Jack Benny Program
The Life of Riley
Life with Luigi
My Favorite Husband (Lucy in a forerunner to I Love Lucy)
My Friend Irma
Our Miss Brooks
The Phil Harris-Alice Faye Show

Dramas:

Dragnet
Yours Truly, Johnny Dollar
The Shadow
Sherlock Holmes
Gunsmoke (William Conrad is amazingly good)

Anthologies:

Suspense
Screen Directors Playhouse (abridged versions of popular movies, usually with one or more of the original stars)
Lux Radio Theater
Arch Oboler's Plays (like the Twilight Zone)

One thing that's surprising to me is the timeline. In my mind, I slways figured that TV came in around 1950, and that this kind of programming quickly fell off. But Gunsmoke had both radio and TV versions runnng from 1955 to 1961, Johnny Dollar was produced till 1962. Have Gun - Will Travel actually started as a TV show, and was successful so they added a radio version. Over about 5 years, Jack Benny slowly morphed from a weekly radio show with occasional TV specials to a weekly TV series.

The comedy seems pretty fresh - there's no line where TV comedy is slicker or more sophisticated. In fact, some early TV I've seen, like the Goldbergs, is more primitive than anything I've heard on radio.

One show that's kind of amazing is Blackstone the Magician. A magician on the radio! He'd star in some mystery and solve it by some little trick, then come back after the commercial to tell you how to do the trick.