The official taxis at ARN are "half-regulated." Meaning that there's a company (can't remember the name of it now) which is running the official taxi stand. They need to approve each taxi company before they can pick up passengers at the ARN official taxi stands. And they basically only approve companies with somewhat normal prices. So all taxi companies at ARN have fixed prices between (from memory) SEK 500-800 to central Stockholm.

But sometimes, "pirate" taxis take up position in other places at the airport, outside of the official stands. And some of those companies may charge EUR 500-1,000 for a run to Stockholm.

Basically, as long as you take a company from the official stands, you're pretty safe.