Examples of type 1 (characters involved in production)
The Disney film Bolt is about a dog who's convinced he has superpowers, because he's actually the star of a TV show whose director believes strongly in Enforced Method Acting.
Or in this case, a Movie Within a Movie, according to Chicken Little. Once originally a story about the title character and his "sky is falling" incident, it was eventually remade into an action-packed science fiction flick.
Examples of type 2 (characters are fans)
The Disney animated 101 Dalmatians has two. The dogs watch the dog-hero show Thunderbolt, and the criminal sidekicks watch What's My Crime?
Cars 2 has The Mel Dorado Show, which is a talk show hosted by a brown Cadillac who for some reason wears glasses over his windshield (eyes) and Tire Talky, a Japanese talk show sponsored by a purple truck who constantly carries a giant Jumbotron on his trailer (the episode shown on the truck's screen is one where Francesco Bernoulli is shown demonstrating his soccer skills in front of the show's host (a Scion XB)).
In The LEGO Movie, Emmet and the other citizens of Bricksburg are all fans of a show called Where Are My Pants?. Later on, Wyldstyle "cancels" it when she hijacks the channel to broadcast a message, flinging a pair of LEGO legs at the male actor as she shoos him away.
"Honey, where are my paaaaaaaaants?"
It's a Parental Bonus, as it's clearly a Lego Porn studio, but the narrator is a child, who didn't understand that and thus made up the ridiculous show.