Check your system keyboard settings. It simply reacts over-sensitive and record multiple hits. Decrease the typamatic rate. If you use a wireless or infrared keyboard, update the drivers and settings to avoid additional delays with bad reception or consider using a conventional cable keyboard.
If you are using a Wacom Tablet then you are another victim of the Wacom/Illustrator bug. As far as I know there is no fix yet. The only workaround is to temporarily use a regular mouse.
Yes, i'm using latest Wacom Bamboo Fun.
I just tried to use my MacBook's touchpad instead of tablet and arrow keys work fine. That confirms the Wacom Tablet bug. It's kinda strange that there's no discussions anywhere on this topic. Hope there will be a solution soon. So now i'll have to use touchpad when i work in Illustrator. Thank you for your answer, it helped.