4. Angel, "She" (Season 1, Episode 13)
As both a spinoff of Buffy The Vampire Slayer and a series with a heavy mythology base in its own right, Angel is not the easiest series to find inroads to. There's always the option of starting with the pilot, "City Of"...but for someone with a casual interest or curiosity, that's not necessarily the way to go. Instead, an episode like Season One's "She" is the choice I'd make. As mentioned, Angel is a mythology-heavy series, especially in its latter seasons. That's all well and good, and there are some truly excellent story arcs (and even individual episodes) to be followed through there. But in Season One, Angel was oftentimes a 'monster of the week' show and "She" is a good example of that approach. Featuring the first official outing of Wesley with Angel Investigations as well as an engaging heroine/foil for Angel, it may not be the most brilliant episode of the series, but it's sure a good place to start.
Honorable Mentions: Somnambulist; City Of.