I Remember Because

The police are questioning a witness. The detective asks for a specific detail, such as the date of a past event or the name of a suspect. This is not something a witness would be likely to remember with precision.

However, the witness does remember, exactly and with certainty. Before we can raise an eyebrow, he explains why he remembers. It turns out he has some connection to the name, date, or other information. The suspect had the same name as the witness's father, or the date was his daughter's birthday.

This is essentially Scotch Tape. It saves everyone the trouble of long, boring scenes where witnesses consult their calendars, go through receipts, or any of the other activities one might do in real life to reconstruct such details. On occasion, though, the witness's offhand statement turns out to be a clue, or sets off a Eureka Moment.

Standard in the Police Procedural.

Examples of I Remember Because include:

Film

In Slumdog Millionaire, the main character is able to answer the gameshow's trivia questions because most of the answers directly relate to memorable events in his life.
Parodied, like so much else, in Clue. As he recounts the night's events, Wadsworth suddenly pauses and answers the question that absolutely nobody was asking.

Wadsworth: I know because I was there.

Live Action Television

Used regularly in the Law and Order franchise.
Can be played for comedy, too. On Friends, Monica tells Joey that Chandler met a woman named Ginger. "I remember because when he told me, I said "the movie star."
- In another episode, Monica remembers precisely what time she ran into Richard despite claiming she's not still in love with him, because she'd been arguing with a clerk over whether or not a movie was late at the time.
In an episode of CSI, a man can recall the exact time he heard something suspicious due to having rented a porno pay-per-view movie scheduled to start at that time.
An episode of Monk has a competitive eating champion who tells Stottlemeyer and Disher that an all you can eat buffet he was at at the time of the crime can back him up because: "Oh, they'll remember me."
In an (in)famous episode of The Practice a witness on the stand Remembered Because she was about to go inside to watch Boston Public at the time - both produced by David E. Kelley. Infamous because earlier that same season there was a Crossover between the two shows, despite them being on different Networks.
Hill Street Blues: A court witness with transactional immunity (meaning he couldn't be prosecuted for any crimes related to his testimony) when asked why he was so sure about a date said "because that was the same day I killed a cop."

Literature

An inversion in the Isaac Asimov short story What's in a Name?, where the suspect who works at the science reference library claims they don't remember the name of a furrier named Ernest Beilstein who inquired at the reference desk at the alibi moment. The detective alleges that she could not possibly have forgotten this due to the coincidence of his sharing a name with Beilstein's Handbook of Organic Chemistry, the canonical sixty-volume encyclopedia of chemical compounds and reactions.
In Chrystine Brouillet's French novel, Les Neuf Vies d'Edouard, a witness remembers the exact time he saw a suspect because he was very worried of running late for his plane at the time. This is particularly unnecessary detail repeated as third-hand information to the reader.
In the Sherlock Holmes story "The Retired Colourman", Watson remembers the number of a theatre ticket because it was his old school number. Making this...
In the novel Anastasia Absolutely, there is an investigation into a bomb found in a mailbox. It's mentioned that one of the letters underneath the bomb was a birthday card, and the police could pinpoint the time it was mailed because the woman who mailed it remembered the song that had come on the radio a moment before.
In Allegiance a young captured pirate says this phrase, but the stormtroopers who captured him don't care why he remembers which day it had been, so they cut him off.

Newspaper Comics

Parodied in a Far Side cartoon—a woman points out a man in a police line-up, saying "That's him! That's the one! I'd remember that dinky little hat anywhere!" The man in question is twice the size of everyone else, with three eyes and a trunk.