A long running series that would commence with a seemingly ordinary situation that would change, there would be a familiar music played and Rod Serling (one of the writers) would walk into the scene and pose the question, is this an ordinary situation or have you just entered the twilight zone. From this point on the show would become mysterious and have a fantastic science fiction bent.
The Twilight Zone is a classic American anthology series that originally ran from 1959 to 1964 on CBS. Rod Serling created the show, wrote a large number of its episodes, and voiced the opening and closing narrations that framed each episode (later turning some of these into on-screen introductions). The show combined speculative genre fiction of all kinds with moral and ethical reflections in a way that has rarely been duplicated, and it has endured in popularity and notability in the many decades since.
Episode themes were a dizzying array, from measuring the human against the inhuman, dealing with the devil, the fallouts of fear, the nature of death, to the power of belief and imagination. Interwoven with these were slightly more standard "what if" plots, ranging from parallel dimensions, visits from beyond, space rockets, and time travel.
A majority of episodes end with a plot twist, often designed to highlight the theme or an aesop, but sometimes just to shock the viewer with a cruel fate, a simple and happy ending being a rarer closing. Certain episodes were notable enough that they are highlighted works in their own right, still prone to discussion, references in other series, and occasional parody to this day ("Time Enough At Last", "The Monsters are Due on Maple Street", and "Nightmare at 20,000 Feet", for just a couple examples).
The series has been revived twice, first on its original network of CBS from 1985 to 1989, and again on the UPN network from 2002 to 2003. A movie was created which was itself an anthology of four separate plots. Finally, a radio drama series was started in 2002.
More information can be found on the Wikipedia page.