My favorite theme song from a 50s TV series is too hard to choose so I will give the three that topped my list.
1)Peter Gunn(no surprise here!)
2)77 Sunset Strip(although, too much hearing it and it could easily move over to the top of my "most annoying" list)
3)Johnny Staccato(although i rarely see the theme song, or even the series itself, mentioned. But, come on, a TV show based on a jazz musician, who also moonlights as a PI, better roll beginning credits accompanied by some sweet buzzing tones!)

Burns & Allen's Love Nest
Just a love nest, cozy and warm,
Like a dove rest down on a farm,
A veranda with some sort of clinging vine,
Then a kitchen where some rambler roses twine,
Then a small room, dream room for two,
Better than a palace with a gilded dome,
Is a love nest you can call home.

I Love Lucy, for sure.
You dodge a question like a character dodges a punch on Mortal Kombat.-IceJJFish

How can we not mention the Naked City theme? That haunting melody is so evocative of the city streets at night.
Perry Mason. It sounds like high class stripper music, with that brassy melody and thumping bass.

I like The Syncopated Clock music and other Leroy Anderson compositions. I don't know if any more of his music was used for TV themes but they are so cozy 1950s especially Blue Tango and Bugler's Holiday.

Rialto Ripples on the Ernie Kovacs Show.
The Syncopated Clock on the Early Show.

I Love Lucy
Volker Flenske: (While torturing David) I don't know why you're doing this to yourself!

Henry Mancini's hard-driving "Peter Gunn" theme, especially the way they made the main title FIT the music, adds to the excitement! (A '60s main title favorite, "Hawaii-Five-0" does a similar "marriage" of music with quick-cut visuals.)
Frankie Laine's "Rawhide" (Keep movin' movin' movin' tho' they're disapprovin')
"Perry Mason" the "threatening" strings at first segue into a piano-beat minor chord theme that can only be called kinky.
"Dobie Gillis"
The Ballad of Wyatt Earp (sung by a barbershop quartet)
"Bat Masterson"
Heck, I can still hum the themes from "Riverboat", "Buckskin" and "Death Valley Days" tho' I haven't heard them in years.

Favorite line: Gottem beads, gottem looking glass. My father-in-law loved that line and my wife picked it up and passed it to me.

Rawhide
And hey guys? Imagine Greater. Josh Gates GH-Live

Even though it was a stock theme from composers John Seely and Bill Loose at Capityol, The Donnas Reed Show theme, TC-430A "Happy Day" or "Domestic"
Of course,
Walter Schumann's "Dragnet theme"
Elliot Daniel's "Lucy"
Fred Steiner's "Perry Mason"

Realized today that Natchez to New Orleans fits a riverboat gambler. But I don't think it was consider "the West" in the era that Maverick portrayed.

My lyric memory is sketchy but here are some I remember.
The lawman came with the sun.
There was a job to be done,
And so they called for the badge and the gun
Of the lawman!
And as he silently rode
Where evil violently flowed
They knew he'd live and he'd die by the code
of the lawman!
or
Riverboat ring your bell.
Fairthewell Annabelle.
Luck is the lady that he loves the best.
Natchez to New Orleans,
Living on jacks and queens.
Maverick is the legend of the West.
or
Have gun,will travel reads the card of a man.
A knight without armor in a savage land.
His fast gun for hire meets the calling wind.
A soldier of fortune is the man called Palladin.
Palladin, Palladin, where do you roam?
Palladin, Palladin, far far from home.
or
Johnny Yuma was a rebel.
He roamed thru the West.
And Johnny Yuma, the rebel.
He wandered alone. (cant' remember what comes after)
I used to sing along, and then I'd sing these songs at odd times between programs. At one time I think I knew all the words of Rawhide. It was sung by Frankie Layne, who was a kid favorite of mine.

Haven't thought about any of them in a very long time:
Lawman
Maverick
Peter Gunn (most famous Henry Mancini tune)
Rawhide
Perry Mason

Most of mine are from westerns:
Cheyenne
Maverick
Bonanza
The Rifleman's closing theme.

77 Sunset Strip
Highway Patrol
Lawman
Tombstone Territory
"You can't send a kid like this up in a crate like that on a night like tonight!"

(1) The crashing chords as you saw the view of the city and night fell diagonally The opening of The Edge of Night as well as the gorgeous piano and organ closing theme played during the credit crawl.
(2) The tempestuous waves hurling at the rocky cliffs displayed during that great tense music for the opening of The Secret Storm. (Visually that image was so great Dan Curtis lifted it a decade later for the opening of Dark Shadows. LOL)
The visuals and the musical themes for the opening of those two shows still make me smile at the recollection. It's tragic today that closing themes and credit crawls no longer exist. Much as I love shows like Lost or The Vampire Diaries, is there any living person who's heard and can humm the musical themes accompanying them?

M Squad, The Millionaire-short opening theme, Perry Mason.

The I Love Lucy theme is my favorite.

1. Peter Gunn (without a doubt)
   Others in no particular order:
   Mr. Lucky (another Mancini)
   The Untouchables
   Perry Mason (extended into the '60s)
   The Twilight Zone
   Alcoa Present One Step Beyond (not so much the theme, but the music that occurs at the time of the psychic phenomenon).
   But throughout it all, my motto was "Dignity! Always dignity!".

The "M SQuad" theme was slightly reworked for "Police Squad!" with Leslie Nielsen. Even the first episode of the second season of "M Squad" was almost shot for shot used as the "Police Squad" pilot.

I like most of the ones mentioned, at least those I remember. I was not a fan of either Lucy or Honeymooners, but I do remember the themes.
No recollection of "Corliss Archer" (except radio)
No recollection of "Rocky King"
I would add to these lists the melodic theme from "Medic," starring Richard Boone as Dr. Conrad Steiner.

"Meet Corliss Archer"
"Rocky King, Detective"
"I Married Joan"
"I Love Lucy"
"The Honeymooners"
All very catchy! I hope I DO get them stuck in my head!
"It's Bucket 'o Nothing! Surprise your friends, amaze your family, annoy perfect strangers!"

It has absolutely GOT to be the theme from 'Peter Gunn', especially the Duane Eddy version.
Holds its own with any of the classic Bond themes.