General:
* Annoy
* Pester
* Nuisance
* Irk
* Vex
* Bother
* Irritate
* Get on one's nerves
* Drive one crazy
* Bug
Informal:
* Tick off
* Get to
* Grub
* Piss off (stronger, potentially offensive)
More specific:
* Nitpick (to focus on minor details)
* Nag (to repeatedly ask or complain)
* Badger (to persistently annoy)
* Harass (to persistently annoy or bother)
The best word to use will depend on the specific context and the intensity of the irritation.