Births
When a established character gives birth, usually because the actress is pregnant in real life. Similar to the New Character category.
Eg: Baby Dill, Rugrats

Deaths
Sometimes a conscious decision by the writers; often due to unfortunate circumstances. Similar to the departure category, but tends to be permanent (some exceptions, for example: Alias).

Eg: Tara, Buffy

Character Departures
Again sometimes a conscious decision by the writers; or due to a dispute with the actor. Usually done in a way that the character can return if need be.
Eg: Fox Mulder, The X-Files

Graduation
The kids grow up and graduate; thus the show ends up catering to a different demographic.
Eg: Riverdale High, Sabrina

Weddings
It's something that the show builds up over many seasons, but tends to be disappointing once it actually happens.
Eg: Lois and Clark, The New Adventures of Superman

The Movie
A successful series tends to spawn to the big screen. Often takes the show to places it cannot return from.
Eg: The plethora of movies based on Saturday Night Live sketches

New Character
Generally a tactic to try and bring in a new audience. Often happens after a Graduation.
Eg: Cousin Oliver, The Brady Bunch

Same Character, Different Actor
Usually a result of a death or dispute. If done well, hardly noticeable (such as Marilyn in The Munsters), however, it does tend to be very jarring for the audience.
Eg: The Two Darrens, Bewitched