"Blink" - Doctor Who
The Doctor is a side character in this episode, but still important. It's a mind trip, and a great stand alone episode that you really don't need a huge backstory...just know that The Doctor is a time traveler. Plus, Carey Mulligan!
"The Body" - Buffy the Vampire Slayer
I'll avoid the big spoiler...just in case. But for a show that deals with the supernatural and inhuman, this episode is written so humanly. Dealing with stuff people have to deal with everyday. And yet, there's humor to it, too.