Note that the completion of vaccinations and vet forms can take 3-4 months, so if you want to take your dog to Sweden, plan early. Tattooed dogs and cats won't qualify after 2011 in favor of microchips.
The most important thing to know when taking your dog to Sweden is that two types of pet regulations exist depending on whether you enter Sweden from an EU country or from a non-EU country. The Swedish Department of Agriculture provides a guide as well. Note that Sweden still requires deworming for tapeworm until at least 2012.
Bringing your dog to Sweden from the EU: First of all, get a EU pet passport from your vet. Your licensed veterinarian will be able to fill out the EU pet passport as required. To take dogs to Sweden from within the EU, the dog must be vaccinated for rabies (test for rabies antibodies by approved labs only and deworming not required after 30 June 2010.)
Do not forget to stop at the customs office when arriving in Sweden so the customs personnel can check the dog into Sweden.
Bringing your dog to Sweden from a non-EU country: Requirements for pet travel are slightly stricter. Like travelers from the EU, you should also get your dog a pet passport if at all possible or have your vet complete the Veterinary Certificate (.doc).
In addition, you will also need a "Third-Country Certificate" available from the Swedish Department of Agriculture. The countries outside the EU is devided in two groups, one is called listed countries and the other is called non listed countries. From the non listed countries Sweden requires quarantine in an approved quarantine-station for 120 days, and also identitymarking, deworming and an import-license.
Taking your dog to Sweden from a non-EU country requires the dog (or cat) to be vaccinated for rabies and Sweden also requires a bloodtest for rabies antibodies taken earliest 120 days after the latest rabies vaccination from countries outside the EU.
Note that in Sweden, dogs and cats from non-EU countries may only be brought in via flights to Stockholm-Arlanda airport or to Gothenburg-Landvetter airport.
When you arrive in Sweden with your dog, follow the 'Goods to Declare' line at customs. Swedish customs personnel will help you with the process and will check the dog's (or cat's) papers.
Tip for booking your dog's flight: When you book your flight to Sweden, don't forget to notify your airline that you wish to take your cat or dog to Sweden with you. They will check for room and there will be a one-way charge. (If you wish to sedate your pet for the trip, ask whether the airline's animal transportation rules allow this.)
Please note that Sweden renews animal import regulations annually. By the time you travel, there may be slight procedural changes for dogs. Always check for official updates before taking your dog to Sweden.