Yeah, the sack of Paris...
In general the vikings that raided western Europe tended to be Danes or Norwegians while Swedish vikings usually headed for the Baltics and controlled the Russian waterways all the ways down to Constantinopel and evendid business with Baghdad. Borders weren't really set though, and large parts of southern Sweden were considered part of Denmark back then. Yet we know from finds of British coins and inscription on rune stones that quite a few Swedes were involved in the expeditions to England.
That being said, Frankish chronicles attest that the attack on Paris was lead by a viking called Ragnar. Traditionally many have attributed this to the legendary Ragnar Lodbrok, who supposedly was a Swedish king. There are many legends about him, but it has been hard to verify him as a historic person. His sons, Ivar the Boneless, Sigurd Snake-eye, White-shirt, Ubba and Björn Ironside are confirmed historical people though and three or four of them were part of The Great Heathen Army that wrecked havoc on the British isles and controlled large parts of it from 865 to 878 AD.
The sagas attribute this invasion to Ragnar's sons wanting to avenge Ragnar's death at the hand of the Northumbrian king Aella in 862 AD.
They supposedly captured Aella and performed "the blood eagle" on him, ie cut off the ribs on both sides of the spines and pulled out the lungs, so that they looked like wings that flap as the air goes in and out of them.
Anyway, Björn Ironside, who is a confirmed early Swedish king and who was the son of Ragnar Lodbrok, who may or not may be the Ragnar who sacked Paris, did actually try to sack Rome in 860 AD.
Unfortunately, there weren't really any big cities in Scandinavia, so Björn and his fleet mistook the city of Luna for Rome, and attacked and conquered it. As they were informed that this was not Rome, they were outraged, burnt the city to the ground and had all the people there either killed or sold as slaves. Heading back toward Spain, after having raided parts of Sicily and the North African coast, they ran into a Muslim armada that sank most of their ships. To boast moral they then conquered Pamplona on their way home.
Anyway, when it comes to thinking big, Carl XII, also attempted to invade Moscow as late as 1707-09. He failed. Then spent five years in Bender, in present Ukraine, negotiating with the Ottoman emperor to convince him to attack Russia together with the Swedish troops. Eventually the emperor declined, and the Swedish army had to fight its way back home to Sweden.
This was supposedly the origin of the Swedish meatballs, as a similar dish, köfte, is rather common in Turkish cuisine.
The Swedish soldiers also grew accustomed to coffee, tobacco and arrak during their extended stay in the Ottoman empire, and brought these habits home with them.
Which brings us to our biggest mistake of all time; the founding of Russia.
As mentioned earlier, Swedish vikings controlled the waterways of Russia, and a group of vikings from the Roslagen area, referred to as Rus, lead by a guy named Rurik, became rulers of first Novgorod and then Kiev as well. Over time the Rus controlled an increasing area, they assimilated with the local slavs, and their kingdom eventually became what we know as Russia. Damn, that one has really come back to bite us in the ass.