Depends on the game, to be perfectly honest.
Normal difficulty will more or less always be the baseline experience, how the game was meant to be played; on the odd occassion a developper might say the hard mode is the intended difficulty (for example, the Halo series on Heroic), but for the most part normal is the design target.
Games which generally don't need difficulty settings are those which lean towards being fairly easy no matter what you do. When the only changes which come out of the difficult settings are enemies having altered toughness and damage outputs, the only thing affected the amount of tedium the player goes through. In games which are relatively easy by design (Fable, for example; The Legend of Zelda franchise is another good one), this is unnecessary; find a nice balance for maximum fun, so that fights aren't too long or too short.
For games which are more action-oriented, difficulty settings make more sense; not everyone has the dexterity needed(or patience to acquire it) to beat the game, so not including an easy difficulty could pretty much kill your game due to it being inaccessible for the average player. This also allows room for higher difficulties as well, at which point a developper can go nuts with what's being thrown at the player (more enemies, different types and combinations, smarter too). In these games, it works.
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Not every game really benefits for difficulty settings, plain & simple; sometimes they don't affect the game in any significant way, which is most apparent when the only thing affected is the amount of tedium involved (nothing more than reducing the margin for error doesn't do much either). What's the point of a platformer having a difficulty setting? Or an enjoyable puzzle-focused action-adventure game?
Some games take to difficulty settings well, others don't.
