Not Carroll.

My first film role was a minor part in Gone With the Wind.
I am most famous for having starred in the title role of a popular TV series which ran from 1952 through 1958.
My death in 1959 remains controversial: was my fatal gunshot head wound self-inflicted due to depression, or was it murder?

George Reeves.

Bingo! George Reeves it is. I had to dance around his role as TV’s Superman, or it would have been an instant giveaway.

I give the matter some thought and post somethihg soon...

I could have continued with “I guest-starred as my most famous character in an episode of I LOVE LUCY” (in the episode “Lucy Meets Superman”).

Gone with the Wind and the questionable suicide gave it away to me. At first I was thinking "Have Gun will travel" ala' Paladin... but the math didn't add up.

1. I was born March 26, 1931.
2. My first major role was at 17, as Ralphie in an amateur production of Clifford Odets' Awake and Sing!.
3. I appeared in Bonanza (1960), The Rebel (1960), Two Faces West (1961), Rawhide (1961), The Untouchables (1962), The Eleventh Hour (1962), Perry Mason , Combat! (1963, 1965), Daniel Boone, The Outer Limits (1964), The Virginian (1963-1965; and Get Smart (1966). Though I am well known for another role.

4. I hosted and narrated a series in search of paranormal or unexplained events or subjects.

5. I won acclaim for a series of stage roles. I played the starring role of Tevye in Fiddler on the Roof, as Arthur Goldman in The Man in the Glass Booth at the Old Globe Theater in San Diego, and as Randle McMurphy in One Flew Over the Cuckoo's Nest.

I actually saw the original New York productions of all three plays you mention above--but that doesn't seem to help me!

Well, I'll take a wild guess at William Devane who was the original stage Randle Patrick McMurphy, but I don't think he fits all the clues.

Leonard Nimoy?

Oh, good guess, karnak!

The hosting of "paranormal or unexplained events or subjects" series made me think of Nimoy as well ...

I recently re-watched a second-season (1964) episode of THE OUTER LIMITS entitled "I, Robot" in which Nimoy appeared. And the reference to being "well known for another role" brought Mr Spock to mind.

I loved that episode Karnak.

Part of that episode was a courtroom drama, which in some ways reminded me of INHERIT THE WIND — with Nimoy’s role paralleling that of Gene Kelly’s cynical wise-guy newspaper reporter E. K. Hornbeck (itself a thinly disguised take on real-life reporter H. L. Mencken). One of my favorite films of all time.

Leonard Nimoy is correct. I had to dance around Star Trek and did a little word play with "in search of"...

I was born in Nebraska on March 27, 1931.
I died in 1980 of a heart attack at the relatively young age of only 48 (a heavy smoker/drinker/workaholic).
I starred in a classic, highly regarded prime-time network TV drama that ran for four seasons (from 1963 to 1967).

Trying to redeem myself...

Mr. Richard Kimble.

If correct?, I'll give the floor over. If not, I'll go in hiding for awhile.

That was actually the name of his character in THE FUGITIVE -- not the name of the actor himself. But that's probably close enough; we know whom you mean.