For all of you who wants to know how to get in to Stockholm in an easy way should either take a cab and use the big companies such as Taxi020 or Taxi Stockholm. Please ask a host that stands in the Taxi remote on how to proceed because there is alot of single cab owners who can rip you off big time if you are not careful.
Please ask for the price before you start and also ask the host what the price should be if you are unsecure with the situation.
The Taxi host is hired by the Airport Auth. so they have no profit to make and is only there to make customers more comfortable with the cab situation at the airport.

You can also use the Express Train to Stockholm called ArlandaExpress.
This train is usually a little bit more expensive but it will take you diretly into Grand Central Station in about 20mins.
It's a good alternative to a Cab especially if you don't have time on your side.

The train cost 190sek and if you are only one person the train is always cheaper and faster then a taxi.

At the Arlanda Express station in downtown Stockholm there are taxis that can take you to your hotel(unless you are staying at Scandic Continental, Radisson SAS Royal Viking or one of the two Nordic hotels beucase then you have walking distance from the terminal).