I think Full House ran the longest family television sitcom. What do you think?

Not even.

Some of the Longest Running Television Comedies

By number of seasons:

18 The Simpsons (Fall 2006)
14 (The Adventures Of) Ozzie And Harriet
12 My Three Sons
11 M*A*S*H, Cheers, The Danny Thomas Show / Make Room For Daddy, Happy Days, The Jeffersons, Married ... With Children, Frasier, King Of The Hill (Spring 2007)
10 Murphy Brown, Mystery Science Theater 3000, Friends, South Park (Fall 2006)
9 The Beverly Hillbillies, The Love Boat, Alice, Roseanne, Family Matters, Coach, All In The Family, Night Court, The Drew Carey Show, Everybody Loves Raymond, King Of Queens (Fall 2006)

By number of episodes:
435 (The Adventures Of) Ozzie & Harriet
387 The Simpsons (Fall 2006)
380 My Three Sons
336 The Danny Thomas Show / Make Room For Daddy
275 The Donna Reed Show, Cheers
274 The Beverly Hillbillies
264 Frasier
259 Married ... With Children
256 M*A*S*H
255 Happy Days
253 The Jeffersons
252 Bewitched
249 The Andy Griffith Show
247 Murphy Brown
245 The Love Boat
238 Friends
234 Leave It To Beaver
233 The Drew Carey Show
222 Roseanne
214 Family Matters
210 All In The Family
209 The Facts Of Life, Everybody Loves Raymond
204 Home Improvement
202 Alice
201 The Cosby Show, King Of The Hill (Spring 2007)
200 Coach
199 King Of Queens (Fall 2006)
193 Night Court, Will & Grace

I would also have to say Full House