At the end of almost every episode of Neon Genesis Evangelion when showing the trailer for the next episode, Misato assures the viewers that there will be more fan service to come.

A famous scene that offers plenty of fan service, is where Asuka is explaining to Shinji about thermal expansion and she asks him if when she cups her breast in her hand, it gets bigger.

Generally speaking, fan service is simply "giving the people what they want."

Xena and Gabrielle sharing a moment of subtext, Trowa and Quatre from Gundam Wing playing music together, the lovingly detailed footage of Voltron forming, or a random yet popular redshirt or bridge bunny suddenly getting lines... Fan service, all of it.

Arguably, the Evangelion movie is an example of fan service for people who dislike fanboys.

In theory, fan service is supposed to reward loyal fans for watching the show by giving them panty shots, toplessness that may lack detail, and suggestive poses. However, the example already noted regarding Evangelion disproves this, because if it was a real gift to the fans, Misato would not warn us ahead of time that there would be fan service in the next episode.

Then again, I'm not aware of any other examples of the fan service warning, so maybe it's just that one show.