For special sweepers - offensive oriented Pokemon that use Special Attack moves - you want modest or timid natures. The former gives you more points in Special Attack, which makes your Pokemon's moves more deadly. To balance things out, they take away points from the Attack stat, which is just fine for special sweepers. The latter gives it more Speed points, which will help you land your Pokemon's moves first. Pokemon like Starmie, Alakazam, and Magmortar excel with modest and timid natures.
Physical sweepers - offensive oriented Pokemon that use moves based on the Attack stat - need high Attack and Speed ratings. Ergo you'll want adamant or jolly natures for these kinds of Pokemon. They'll add boosts to Attack and Speed, respectively, while taking away points from Special Attack. The fearsome Tyranitar packs a huge punch with an adamant nature, while the mighty Electivire becomes even mightier with a speed boost from the jolly nature.
Defensive Pokemon have quite a few options. For these Pokemon, you'll have to see which how their Defense, Special Defense, Attack, and Special Attack are balanced. A physical wall like Skarmory benefits greatly from the impish nature - it boosts its already high Defense, while taking away from its Special Attack, which it doesn't really need since its offensive moves are physical. Vaporeon is best served by the Calm nature, which gives it a boost in Special Defense, while taking away from its Attack, which it doesn't need since its best offensive moves are based on Special Attack.
On a side note, we're so disappointed that naughty is a useless nature. It's fun to say that your Pokemon is naughty by nature (not 'cause I hate ya!), but it's just not a beneficial nature for competitive play.
