"File 13" is a euphemism for the trash can. The phrase is especially used in the U.S. military, and is less common outside of the United States. In the United Kingdom, for instance, the expression "round file" or "circular file" is more common (in reference to trash cans typically being round). Many Unix-like operating systems have a similar reference known as /dev/null. Expressions such as "I'll place that memo in file 13" are often heard in offices as a joking way of saying, "I'm going to throw away that memo." 
The first known citation of "File 13" was in 1941. The phrase's origins may perhaps be traced to 13 being a supposedly unlucky number, although the exact source is unknown. Another explanation refers to the fact that there are 12 months in the year, and a file is typically kept for each, with the 13th file being non-existent (the garbage can A.K.A the trash can where you throw out garbage.). An explanation given in the NZ military is based on the use of stencil lettering, where a capital B (as used for 'bin') looks like a 13. Or the possibility that trash cans were huge.
Usage in popular culture
File 13 is one of the simple games distributed in Dragon magazine. In this board game, players assume the roles of game publishers and each attempts to develop and market "hot item" games before the others.
File 13 was used as a band moniker by Doug "Double Dee" DiFranco of Double Dee and Steinski and record producer David Witz when they released a 12" single on Profile Records in 1984 called "Taste So Good." The track was built with samples from phone sex tapes and too racy for radio airplay although it was a minor hit in dance clubs. Witz revived the File 13 name again in 1988 for a 12" single called "Party Line" also on Profile Records. This track similarly used samples recorded from party lines which were fairly common in older telephone systems. This track failed to chart or sell well and Witz retired the File 13 name for his dance tracks.
In the band A-ha's music video for "Take On Me", the band is depicted as characters in a comic book which is being read in a cafe by the female protagonist. In the video, the comic book comes to life and she is pulled into its world. The waitress at the cafe, thinking she has left without paying, angrily crumples the comic book up and throws it in the trash. Subsequent to this, the band and the girl are pursued in the comic book world by sinister characters in hard hats that have the number "13" printed on them.