A standalone episode refers to a single episode (or two parter) that deviates from the normal format of a series and, sometimes, puts a hold on the progression of the plot altogether for one specialized episode. Characteristics of these episodes may be a lack or absence of the main character and instead focusing in extremely minor characters or new characters introduced within the episode. I like to offer up these episodes as mini movies or as a hook to get one of my friends to start watching a show. You don't need to know anything about what's happened in the series so far since the episode can 'stand alone'. So my friends who don't want to bother to finish an entire series can just sit back and enjoy the characters and worlds I have come to know and love with me.
(note: the list is not in any particular order)
1. "Double Lips" - ep. 3 from Paranoia Agent
This was actually the first full episode I saw from the series. I caught bits and pieces scanning past adult swim and never gave it a closer look. It seemed too weird. But after I finally sat down and watched this entire episode, I was hooked. The weirdness finally made sense and this episode is great example of the series' psychological exploration. The episode focuses on Chouno Harumi struggle to maintain the life she's created, but with the angle of a psychological thriller.
2. "Blink" - ep. 10 s. 03 from Doctor Who
The interesting thing about this episode is that I think it might be more mysterious if you haven't seen any other Doctor Who episodes. Though he's barely in it, the Doctor pops up as this mysterious figure who the main characters of the episode know nothing about. The plot is full of twists and unexpected turns and borders on horror toward the end. The suspense of the final scene had me literally leaping out of my chair and pacing the room yelling "What the hell's gonna happen!".
3. "Expose" - ep. 14 s. 03 from Lost
This episode takes a break from main plot to explore the backgrounds of two minor characters; Nikki and Paulo. In keeping with Lost's non linear storytelling, Nikki and Paulo's story starts at the end. Then it weaves the events before the opening scene with even deeper flashbacks telling how they got on the island in the first place. It tells you how their story ends at the beginning of the episode, but all is not what it seems.
4. "Serenity" - ep. 01 from Firefly
This one might be cheating a bit since it's the first episode and therefore an introductory episode, but I truly believe that it can stand alone. The two part episode (considered a single episode as a whole) almost seems more like a micro-mini-series or tv movie. It has a beginning, middle, and end and, though it ends with out fully explaining every mystery, it still leaves you with the sense of a conclusion. It is especially fun not knowing who the villain of the story is in the beginning since the plot focuses on Mal's (the 'hero' of the series) trust or lack of trust for the people on bored his ship.