Well, there can't be 100% continuity, as Bart and Lisa would be in their 40s by now. Probably the main reason animated shows last much longer than live-action shows is, the reasons for the people watching the live-action shows, especially with children, don't exist after a few years. Nobody cared about Leave It to Beaver when Beaver was about to start high school. The Brady Bunch tried to fix this with "cousin Oliver," but that backfired on them; the same with Eight is Enough and Jeremy (Ralph Macchio's first major role in anything), and Diff'rent Strokes and Sam. On the other hand, the Simpsons, the Griffins (to a point), the Belchers, and the Smiths don't get any older.
That being said, what I don't like is "selective continuity" - for example, while Bart, Lisa, and Maggie don't get older, some of the people around them (Sanjay's son Jamshed and Selma's daughter Ling come to mind) do. Marge didn't go to college - oh, wait, yes she did, for four years. That's not the "real" Seymour Skinner - oh, wait, yes it is - but is Seymour his first name, or his middle name (the diplomas on his wall in "Who Shot Mr. Burns? Part 2" say "W. Seymour Skinner," as part of the whole WS/MS angle)? How old was Grampa when Homer was born - even if he was 16 on V-J Day (and even that contradicts his being in the Flying Hellfish), that makes him born in 1929, so he would be in his 90s, which means he was in his 50s when Homer was born.