THE KONAMI CODE
  Up, Up, Down, Down, Left, Right, Left, Right, B, A
  (then Start - or Select, Start for two players in Contra)

First appeared in Gradius (NES, 1986) because the developer could not finish his
own game while testing it. Reused in Contra (30 lives), Castlevania, Teenage
Mutant Ninja Turtles and hundreds of others - including as an easter egg on a
great many websites.

OTHER CLASSICS
  Mortal Kombat (Genesis)   A, B, A, C, A, B, B  on the code screen - enables blood
  Sonic 2 level select      19, 65, 09, 17 in the sound test
  Minecraft                 /gamerule keepInventory true   (not a cheat as such,
                            but the single most-searched one)
  SimCity 2000              "FUND" repeatedly for a bond offer
  Doom                      IDDQD / IDKFA  (see the Doom list)

The Konami Code on a web page is still a common easter egg - it is usually bound
with a keydown listener comparing against:
  [38,38,40,40,37,39,37,39,66,65]