So, prior to 1523, pretty much all of Scandinavia was ruled by the Danish king as the Kalmar Union - that is, the king of Denmark was also the king of Sweden and Norway. Sweden gained its independence then and took a few chunks of modern Norway, becoming the dominant regional power in Scandinavia.
This is all a bit early for 'colonial times', but this is primarily for background, so you understand why I'm mainly discussing Sweden here.
In 1611, four years after the founding of Virginia, Gustavus Adolphus becomes King of Sweden at the age of 16. A reformer and general of incredible energy and intelligence, he turns Sweden into one of the Great Powers of Europe. At the time, the 30 Years War was raging to determine the role of Protestants in the Holy Roman Empire.
A Protestant nation, Sweden aligns itself wit Britain, Prussia, France, Denmark, and the Netherlands and brings its army to the Pomeranian coast to join the battles in what is now Germany.
Sweden CLEANS UP. Much of this is ascribed to Adolphus himself, who was a brilliant commander (later admired by Napoleon and Clausewitz), but also pioneered many advances in military science. Particularly, his use of combined arms have led some to call him the father of modern warfare.
He also improved the strength of Sweden's central administration and weakened the power of the nobility, creating a government that exemplified later trends in the early modern era.
Additionally, the rising importance of firearms and metallurgy meant that Sweden was making bank off of the Falun Mine, also known as the Great Copper Mountain. This one mine provided as much as TWO-THIRDS of all of Europe's copper - at its peak, that's 3,000 tonnes of copper PER DAY.
So, under a brilliant commander with the most advanced military science in the world and gobs of cash, Sweden managed to end the war with new territories in Pomerania, helping them control Baltic trade.
After the death of Gustavus Adolphus aka the Golden King aka the Lion in the North, the nobility grew in strength under a series of minor monarchs. In 1655, Sweden invaded what are now the Baltic countries of Estonia, Belarus, and Lithuania in the Second Northern War. Sweden took land from both Denmark and Poland-Lithuania, weakening its regional rivals until the 1680s, when Charles XI took back a lot of the land the nobility had taken over the years. Falun Mine also collapsed around that time (after nearly a thousand years of operation, on one of two days a year it was empty - crazy). Then the king died, leaving his underage son on the throne.
A few years later, most of the losers from the 1655 war declared on Sweden. The empire was held together for a while, but by 1706 Sweden was once again relegated to a regional power, forced out of its holdings on the southern Baltic coast.
Sweden never had extensive overseas colonies, and Denmark-Norway was mostly limited to colonies in the North Atlantic, so neither really interacted too extensively with the American colonies, and both were occupied with their mutual rivalry for most of the colonial period.
Follow up: What where American-Swedish relations like during colonial times , if there were any?