What about characters who showed up mid-series and acted as if they had been there all along? Or at least they don't explain their arrival. In their first episode, they're just there and there's no mention of them being new.

Paige on "Ellen." She joined the show in its second season but they made it seem as if she had always been one of the group.

A few of the replacements on "Saved by the Bell: The New Class" - Bobby Wilson (Season 2)... I won't count Rachel Meyers because even though she joined the show in season two, she guest starred in a season one episode, establishing her existence before becoming a cast member.... Eric Little (Seasons 4-7)... Katie Peterson (Seasons 4-7). Those characters debuted and acted as if they were always part of the group. In the case of Eric and Katie, in their debut episode they were both sad to learn that Tommy D. and Lindsay were no longer going to Bayside. Even though they never appeared in an episode with those two. They were the replacements! Ha-ha.

I'm having trouble thinking of more. Anyone else have some?

I used to watch so many shows as a kid but for the life of me I'm drawing a blank right now.

Sondra Huxtable on The Cosby Show - She didn't appear until the middle of the first season making Cliff and Clair the parents of 5 kids instead of 4.

In the pilot episode this conversation takes place:

Clair: Why do we have four children?
Cliff: Because we did not want five