Well it's kind of hard to define most successful... Is it impact on society, ratings, length of runtime, etc...
I'll list most of them I remember watching as a kid or at least watched an episode of (some of which have listed here before). My list doesn't include cartoons, gameshows, or reality shows:
Get Smart (1 of my favs)
Mr. Ed
Dick Van Dyke
Mary Tyler Moore Show
I love Lucy
Green Acres
Lassie
The Lone Ranger
Father Knows best
Brady Bunch
Gilligan's Island
Cheers
Twilight Zone
Hogan's Heros
Three's Company
The Golden Girls (1 of my favs)
The Beverly Hillbillies
Love Boat
The Honeymooners
M.A.S.H
Dobie Gillis
The Munsters
Peticoat Junction
Bonanza
Dallas
The Waltons
Leave it to Beaver
Little House on the Prarie
The Jeffersons
Sanford and Son
Laverne & Shirley
Growing Pains
Happy Days
Lost in Space
Family Matters
Perfect Strangers
Mork & Mindy (1 of my favs)
Wings
Coach
Step by Step
Who's the Boss
All in the family
Cosby Show
Charles in Charge
Night Court
Kung-Fu the legend continues
Highlander
The Incredible Hulk
Family Ties
Knight Rider
Murphy Brown
Alf
Mr. T
Miami Vice
Hawaii 5-0
Home Improvement
Married with Children (my fav of all time)
Simpsons
The X-Files
Roseanne
Ellen
Seinfeld
Melrose Place
Beverly Hills 90210
Saved by the Bell
Full House
The Wonder Years
McGyver
Frasier
Martin
In Living Color
Fresh Prince of Bel Air
Will & Grace
Third Rock
Buffy the Vampire Slayer
Boy Meets World
Diagnosis Murder
ER
NYPD Blue
Chicago Hope
Lois & Clark
Friends
The 70's Show
Drew Carey
Just Shoot Me
Hercules
Zena
Dr. Quin Medicine Woman
Dharma & Greg
Aly McBeal
Dawson's Creek
Oz
Sopranos
Weird Science
2 1/2 Men
Mad Men