Taxies are very expensive in Stockholm, you might also be cheated, so try to avoid them
Fun Alternatives: In the city centre you don't really need anything, further distance use the Subway when possible, it is very easy system to find your way.
I will say if you need to go from point A to point B, rather take the trains & busses. We took a taxi last week & they rip us off big time!!
Unique Suggestions: Make sure of the rate before you take the taxi.
Fun Alternatives: Use the tunnalbana, Commuter trains & busses before you take a taxi.
Taxis. Always negotiate the price before start. The prices may vary quite and the limit is the sky. Use one of the reasonable taxi companies like 020 Taxi, Taxi Kurir or Taxi Stockholm. You may have problems with others, but not necessarily. Anyway, it's up to you.
A ride from Arlanda (airport) to Stockholm could be about 450SEK. Ask for 'fast pris' (fixed price).