One True Love

The most indomitable of story telling romantics is the idea of one utter perfect specimen who is your ultimate match. Perhaps they will have everything in common with you and share your dreams. Often Love At First Sight comes into play when the persion is beautiful. Destiny or The Power of Love are often invoked invoked to explain why that person is the way they are or how you met them.

"All of our young lives we search for someone to love. Someone that makes us complete. We choose partners and change partners. We dance to a song of heartbreak and hope. All the while wondering if somewhere, somehow, there's someone perfect who might be searching for us."

—Kevin Arnold, The Wonder Years

Not to be confused with One True Pairing which is what the fans want to happen. This only applies to examples where it's made clear and deliberate in the work, regardless of what the editor happens to ship and regardless of how convinced you are.

Examples:

Film - Live Action

The Princess Bride: Buttercup and Westley
Sleepless in Seattle: Lampshaded by Annie in one scene who says it is usually invoked as means of explaining all the romantic accidents. Played straight when she later goes along with the idea that Sam is the one anyway.
When Harry Met Sally: Mentioned by Sally complains of a man she was interested in finding his perfect match. "He just met her... She's supposed to be his transitional person, she's not supposed to be the ONE."
Enchanted: Prince Edward and Giselle believe they are each other's. But it's Robert who awakens Giselle.

Live Action TV

The entire premise of How I Met Your Mother is based around Ted's search for his future wife, who has been shown to have the exact characteristics that Ted is looking for.
Raising Hope: Virginia and Burt have remained married for over 20 years, despite Maw Maw continually trying to break them up, because she wanted to boot out her freeloading family. Jimmy later narrates that "if two people are meant to be together, they will stay together no matter what tries to get in their way" - while deleting a text message on Sabrina's phone from her boyfriend, asking her to go to a restaurant, so he could take her out to eat instead.
Played for Laughs for an entire series of Peep Show, where Once an Episode Mark has decided that each and every girl he meets is the perfect woman for him.
Parodied in an episode of Friends: Phoebe asks Chandler if he believes in soul mates. He doesn't, he believes in falling in love, but not that there's one person who's perfect for you. She says "Good, because I just met Monica's!" The rest of the episode is him feeling increasingly threatened by this guy, until Monica explains she doesn't believe in One True Love either.

Monica: I don't think that you and I were destined to end up together. I think that we fell in love and work hard at our relationship. Some days we work really hard.

Babylon 5 has John Sheridan and Delenn, despite the fact that she was his Second Love. The Power of Love between them has been enough for Sheridan to defy both death and torture and may in fact be responsible for winning two separate wars.
- From the same show: Jeffrey Sinclair and Catherine Sakai.

Literature

Bella and Edward in Twilight are repeatedly stated to be this. Many have commented on how their relationship is unintentionally abusive, but if you accept from the word 'go' that they are each others's one true love, their behaviour towards each other is romantic. (If you don't, it looks a lot like stalking.)
- The intent behind an abusive behavior does not automatically make it non-abusive. How many domestic abusers tell their partners their controlling, conniving, violent ways are because "I love you"? It's still abuse.
"Lifemates" in the Liaden Universe are rare but when they do happen, that 'verse's science of psionics can objectively verify it. (It is eventually revealed that this is due to genetic spiritual meddling by Sufficiently Advanced Aliens in the past, and there's a damn good reason why it always seems to happen to the "dramliz" and not anyone else.)
In The Dilbert Future, Scott Adams Deconstructs the trope, pointing out that the One True Love is always within driving distance, and of the preferred gender, age, and species. And if the relationship doesn't work, the person usually will find their "True" One True Love under the same circumstances.

Webcomics

In Homestuck, this is apparently one of the cornerstones of the troll concept of romance. While trolls change lovers around much like humans do, trolls all believe that they have one perfect person (or in one case, two perfect people) for each of the four quadrants of their romance (romantic love, romantic hate, romantic guardianship and romantic mediation). This is called Troll Serendipity (in reference to that specific movie).