Families that brought an additional character to live in their home:

Growing Pains-Luke
7th Heaven-Martin
All in the Family-Stephanie
Brady Bunch-Oliver
Cosby Show-Pam, Olivia
Roseanne-David, Mark
Eight is Enough-Jeremy
Donna Reed Show-Trisha
My Three Sons-Ernie

Are there others?

Didn't Ann Romano adopt that annoying Alex character on "One Day at a Time"?

The Walton's - Rose, Serena, Jeffrey
Diff'rent Strokes -Maggie, Sam
Family Matters - 3J

One Tree Hill-Sam
The Facts of Life-Andy adopted by Beverly Ann
Gimme a Break-Joey

Oliver The Brady Bunch

Happy Days - K.C. Cunningham, Roger Phillips (before he got his own place and Flip stayed with him for awhile), Lori-Beth Allen Cunningham (for a couple of seasons).

The forgettable "Seven" on Married with Children

Didn't Ann Romano adopt that annoying Alex character on "One Day at a Time"?

Please don't remind me of that annoying brat!!

A sure sign of an aging show is to introduce new "family" members, particularly kids.

Little House On The Prairie: Albert, James and Cassandra.

7th Heaven, before Martin wasn't there Robby? That Camden house had a revolving door.

Webster - Nicki
Who's the Boss? - Billy
ALF - Eric
Growing Pains - in addition to Luke, they also had...Chrissy
Moesha - Dorian

Head of the Class: T.J., Billy, Jasper, Vicki, Alex
All in the family: Stephanie Mills
Melrose Place 2.0: Amanda Woodward
A Different World: Lena, Charmaine, Gina, Dorian, Terrell
What's Happening: Little and Big Earl, Snake
Fame: Cleo, Dusty,Nicole, Michael