Why are cheat codes programmed when designing games?

Answer 1

Cheat codes are usually present in games because the developers wanted to test certain features of games to make sure that all aspects of a game work properly. They were much more prominent in older games, i.e. Contra and Sonic the Hedgehog. Many times they are in the final release of the game by accident, because the development team did not have time to close access to them. Other games, such as Guitar Hero or Mercenaries, use them to allow a different play experience without hacks that could break a game (such as Guitar Hero's "Performance Mode" which removes the "highway") or as a comical reference (such as the inclusion of Indiana Jones in Mercenaries, both were produced by LucasArts).

Other "cheat codes" are actually glitches, and activating them can cause irreparable damage to your save file (most famously the Missingno. cheat in Pokemon Red/Blue).

Answer 2

They are usually made for just having quick fun before going back to your normal saved game, but there are other uses. Sometimes if somebody just can't get further in the game they can use cheats to get to see the story in it.