The incorrect use of "its" and "it's".  "It's" is not the possessive of "it".

The use of an apostrophe in a plural noun.  These are pet peeves, not pet peeve's, people.  These peeves of mine possess nothing.

People who persist in driving in the left lane of the highway (the "passing lane").  It's even worse when they drive slowly.

People who don't use turn signals.  Their use is mandated by law, and it's only polite.

People who type with the Caps Lock key on. DON"T YOU KNOW THAT IT"S REALLY ANNOYING AND HARD TO READ? See what I mean?

The plastic wrap and sticker seals on CDs.  Darn near impossible to get off.

Those advertising mail-in cards found by the dozen in every magazine.

People who start writing out their check after all of their items have been rung up by the cashier.

Plastic bags at grocery stores.  Why not just dump everything in the trunk, since it all falls out of the bags anyway?

People who stand on the people-movers (moving sidewalks) at airports.  They're designed for people in a hurry, not for those too lazy to walk 100 yards to their gate.

People who use (and believe) the saying "those who can, do...those who can't, teach".  This is a mindless knock on educators, typically used by those who can neither "do" nor "teach".