Going to the Store

A stock excuse for going out, when a character either doesn't want to give the true reason or is leaving not to return, is "I'm going to the store". In Manga, Anime and other Japanese media, the store in question is likely to be referred to as the konbini; i.e., the local convenience store open at practically all hours.

One reason this trope is a lot more prevalent in Japanese media is that they don't have a lot of space in their homes for storage, and convenience stores sell more kinds of things, so it happens more in Japan.

In the U.S., though, going to get cigarettes or milk or "the paper" is often a convenient excuse to get a character away from the others for a while, and as there are convenience stores that are open 24 hours a day, too, it's not a major expedition, so one character may go alone.

"Convenience Store" is a favoured song for making MAD movies, especially on Nico Nico Douga. Here is an Earthbound MAD.

Anime and Manga

Great Teacher Onizuka: When Anko goes out to meet Noboru, she tells her mother that she's going to the store. Her mother wonders "You took a shower to go to the store? And is that my perfume?"
The Girl Who Leapt Through Time: Makoto uses it as a pretext to go out to test her time-leap ability.
In the Slayers OVA "Jeffrey's Knighthood", Jeffrey's father left to get milk and disappeared for ten years. Presumably he was trying to get away from his crazy wife Josephine.

Film

Betelnut Beauty: Fei-fei, about to run away from home, claims she's going to the convenience store to get past her mother.
In Corrina, Corrina the titular character's husband left to the store to get cigarettes and never came back. The little girl, upon being told this, is afraid this might happen to her dad, who smokes.

Live Action TV

Jackie uses this excuse in one episode of That '70s Show (she actually goes to make out with Hyde).

Jackie: Um, you know, I just remembered that I have to go to the mall because they're having this big Monday Madness sale.
Donna: Jackie, it's Tuesday.
Jackie: See? Total madness!

Will's dad in The Fresh Prince of Bel-Air.
Same for Phoebe's dad for his 2nd family. He went to the drugstore 4 years ago, so he should be back any minute now.
It was a cliché in mysteries for a long time: "What really happened to your husband, Mrs Quigley?" "He went out to get cigarettes six years ago, but he never came back!"
iCarly uses this quite often. One of the more blatant examples is shoving Sam out to buy meat, so that Carly and Freddie can discuss the face he's not had a real First Kiss. Only for Sam to realise she has no money, and come back and overhear the conversation.
Seven's parents went to "get cigarettes". Al notices they used the excuse to leave town and leave Seven with them.

Stand Up Comedy

Ray Romano discussed how he would volunteer for chores if he needed to leave the house. These included stopping by the DMV or applying for jury duty.
Similarly, Louis CK has a story that starts: "Once, my wife sent me to the store to get toilet paper. Because we were out of toilet paper. Because I had thrown it all in the garbage so I could get out of the house."

Western Animation

Nelson's dad from The Simpsons went to the store a few years back and never came back. It is later revealed that he didn't intend to disappear, but he ate peanuts, causing him to puff up and get abducted by a circus passing by.

Comics

In the comic strip Stone Soup, Joan's ex-husband Leon went to the store for some milk and didn't come back. Rumor has it that the store was in the Bahamas.

Real Life

This happened with Stephen King's father.
- ...he went to the store?
  - Yes, to get cigarettes. That was sixty years ago.
This is a Christmas Dead Horse Trope (or possibly a Dead Unicorn Trope) in Sweden. On Christmas Eve, the father in the family uses the excuse of "I'm going to the store to buy a newspaper" to sneak off and dress up as Santa Claus.
- Played for laugh in a christmas special where Santa ended his visits by going to the local store to tell all the dads they could go home now.