That is definitely a tough question. When it comes to TV series I am a kid. My favorites are all cartoons.
The one series that stands out most in my mind would have to be The Simpsons. This series has been going for most of my childhood and it has just stuck with me. It has as many as 14 seasons, which is the most any cartoon has ever run. This isn't just any cartoon though. In fact, it not really considered a cartoon because it's on the fox network and is, I guess, more sophisticated than a normal cartoon. The episodes are laid out as in a soap opera, each having more of a plot than the norm of cartoons. The Simpsons revolves around a somewhat dysfunctional family.
They face the same problems that any average family would face. The episodes delve into just about every problem a person could face. Anywhere from gambling, alcoholism, parent abuse, poverty, hunger, etc. Because the family faces these problems they appear more realistic and almost like a neighbor being followed with cameras. The family consists of Homer, the loving but not so good dad, Bart, the son who always pulls some prank to get into trouble, Lisa, the daughter who would be perfect if her family was not holding her down, and Marge, the loving wife and mother who tends to nag. The Simpsons live in Springfield, which is a fictitious city in the show but is an actual city in real life somewhere. In the show there is a whole world of people created. From the doctor to the drunk to the guys on TV.
Everyone is well known and has names and backgrounds. The show sometimes shifts its interests from the Simpsons and delves into the lives of the other members of the town of Springfield. I really like this show because of the depth of character it goes into and the antics of the hilarious Homer Simpson.