I’m continually amazed what’s available on YouTube, all for free. I stumbled onto an amazing collection posted on the site under the name “Classic TV.” There are literally hundreds of full episodes of some of the most obscure television shows in history, some of which I have to admit I’ve never heard of. And I was practically raised on the tube. 
 
But anyone who grew up in the early days of the medium - especially the late 50s - will definitely recognize at least some of them. (Good luck finding anything you really want to see or, conversely, having the time to see it all.)
 
Here’s the link to where you can find full episodes of this partial list of titles.
 
Jack Benny Show
The Lucy Show
The Dick Van Dyke Show
The Adventures of Robin Hood
Burns & Allen
The Beverly Hillbillies
Petticoat Junction
My Little Margie
Dragnet
Meet Corliss Archer
Mack & Myer For Hire (shorts)
I Married Joan
Private Secretary
Bonanza
Suspense
Thriller
Lights Out
Climax!
Studio One
Telephone Time
Date With The Angels (Betty White)
Life With Elizabeth (another Betty White show)
Tales Of Tomorrow (early Twilight Zone-type sci fi)
One Step Beyond
The Adventures of Ozzie & Harriet
Annie Oakley
Roy Rogers
The Gabby Hayes Show
The Lone Ranger
The Cisco Kid
Sgt. Preston Of The Yukon
The Last Of The Mohicans
You Bet Your Life (Groucho Marx game show)
Topper
Rocky Jones Space Ranger
Captain Z-Ro 
Sheena Queen Of The Jungle
Tate (Western)
Queen For A Day
Michael Shayne Detective
Medic
Man With A Camera (starring a very young Charles Bronson)
The Loretta Young Show
Gang Busters
Flash Gordon
Dick Tracy
Cowboy G-Men
Captain Gallant Of The Foreign Legion
Adventures of Jim Bowie
Adventures of Kit Carson
Adventures of Champion
Adventures of Sir Lancelot
Terry & The Pirates
26 Men (Western)
Stories of the Century (another Western)
Mickey Rooney Show
Four Star Playhouse
The Trouble With Father
The Star & The Story
Captain David Grief
Stump The Stars (Game Show)
Lawless Years
Boston Blackie
Sheriff of Cochise
Public Defender
Mr. & Mrs. North
Judge Roy Bean
Buffalo Bill Jr.
Dusty’s Trail (with Bob Denver)
Frontier Doctor
Racket Squad
Fury
Lock Up
My Hero
Love That Bob
Martin Kane
Passport To Danger
Ramar Of The Jungle
Shotgun Slade
Hudson’s Bay
Dangerous Assignment
Federal Men
Foreign Intrigue
Sherlock Holmes
Decoy
Range Rider
The Buccaneers
 
Just to name a few!