As [oded][1] mentioned, the 80 column screen is a direct consequence of the IBM's 1928 [80 column punched card format][2].

From the wikipedia page on [punched card][3]s:

>### Cultural Impact
>* A legacy of the 80 column punched card format is that a display of 80 characters per row was a common choice in the design of character-based terminals. As of November 2011 some character interface defaults, such as the command prompt window's width in Microsoft Windows, remain set at 80 columns and some file formats, such as FITS, still use 80-character card images.

Now the question is, why did IBM chose 80 column cards in 1928, when [Herman Hollerith][4] had previously used [24 and 45 column cards][5]?

Although I can't find a definitive answer, I suspect that the choice was based on the typical number of [characters per line][6] of typewriters of the time.

Most of the historical typewriters I've seen had a [platen][7] width of around 9 inches, which corresponds with the standardisation of paper sizes to around 8"-8.5" wide. <sup>See [Why is the standard paper size in the U.S. 8 ½" x 11"?][8] and [History of ISO216 *A series* paper standard][9].</sup>

Add a typical typewriter pitch of 10-12 characters per inch and that would lead to documents with widths of between 72 and 90 characters, depending on the size of the margins. As such, 80 characters per line would have represented a good compromise between hole pitch and line length while maintaining the same card size.

  [1]: http://programmers.stackexchange.com/a/148678/22493
  [2]: http://en.wikipedia.org/wiki/Punched_card#IBM_80_column_punched_card_formats_and_character_codes
  [3]: http://en.wikipedia.org/wiki/Punched_card#Cultural_impact
  [4]: http://en.wikipedia.org/wiki/Herman_Hollerith
  [5]: http://en.wikipedia.org/wiki/Punched_card#Hollerith.27s_punched_card_formats
  [6]: http://en.wikipedia.org/wiki/Characters_per_line#History
  [7]: http://en.wikipedia.org/wiki/Platen
  [8]: http://www.afandpa.org/paper.aspx?id=511
  [9]: http://en.wikipedia.org/wiki/ISO_216#History