Rather than just being a superficial personality, Natures actually affect the growth of a Pokemon. Each nature increases one of its stats by 10% and decreases one by 10% (by the time it reaches level 100). Five natures increase and decrease the same stat and therefore have no effect.
In most cases it is preferable to have a nature that decreases either Attack or Special Attack for Pokemon whose strengths are the opposite type of attack. Espeon, for example, favours Special moves, so it's best to use a nature that decreases its Attack since it won't be used.
Adamant
Bashful
Bold
Brave
Calm
Careful
Docile
Gentle
Hardy
Hasty
Jolly
Lax
Lonely
Mild
Modest
Naive
Naughty
Quiet
Quirky
Rash
Relaxed
Sassy
Serious
Timid