Sweden's greatest strength in the 17th and early 18th century was the fact that it had an exceptionally well trained and well led army. Indeed, a great portion of their resources in both manpower and money were directed at the training and equipping of this force. However, Sweden was always at a disadvantage in terms of what material and manpower was available to them as compared to the rest of Europe. This meant that their ability to absorb losses in either manpower or leadership (in this case, kings) was highly limited. Their rise coincided with great victories, and their fall coincided with an exhaustion of their material and human resources and poor leadership that could not be overcome. Without a near constant string of good leaders and exceptional military victories there was no way Sweden was ever going to be able to maintain their status as a Great power. For perspective, let's compare the populations of the various great powers circa 1700:
You'll notice the final one represents a similar number to Sweden, and the kings of Prussia also had to rely on both excellent leadership and a high quality army to make up for their smaller size. However, not only did Prussian luck continue far longer than Swedish luck, Prussia also was successful in expanding their reach, particularly into Germany itself. This increased their population rapidly. Meanwhile, Sweden had the unenviable task of holding a large territory of foreign peoples directly bordering two major powers. Russia in particular, with its vast manpower, simply needed to drain Sweden dry. Prussia's luck allowed them to recover whenever something similar happened. Sweden's did not.
There is one final aspect to this story as well. Sweden's military misfortunes combined with an already more democratic system than other places meant that over time the king's power was sharply reduced. The Swedish people grew tired of war, and the king lost the power to really push them farther. This is compared to, say, Prussia for example, where democratic reform similar to Sweden's took much longer.
I saved this post to answer it later but then I forgot about it until now. Derp. Anyway, hoping I'm not too late...
What events led to the rise of Sweden as a great power in the mid-17th century?
If I had to choose a single event that set in motion Sweden's rise to power in the first half of the Seventeenth century, it would be the fall of the Order of the Livonian Knights around the half of the Sixteenth century. The subsequent power vacuum in the region - which consists approximately of the odiern contemporary Baltic Republics, Lithuania, Estonia and Latvia - gave Ivan IV, tsar of Russia, the chance to seize an access to the Baltic sea; and so he did, conquering Narva in 1559. Denmark and Poland also showed interest in the region; and while Sweden had no quarrel with Poland - not yet! - it definitely coudn't allow its two major enemies to control the Baltic harbors. So when the city of Reval, worried by what was happening, asked to be put under swedish protection, Eric XIV, King of Sweden, gladly accepted. From there, the Swedes were able to expand their control on the area, conquering Narva in 1581; the peace of Teusina, signed by Russia and Sweden in 1595, estabilished swedish control over Estonia.
So the first stone in the building of the Swedish Empire was set; and after this war, Russia itself was no longer a threat, at least for a while. But the conquest of Estonia also meant new trouble: Poland had been acknowledged by Russia in 1583 control over Livonia - which, the way they saw it, included Estonia. To solve the issue peacefully, the polish magnates elected Sigismundus, heir to the Swedish throne, as their king in 1583; doing so, they hoped they could convince Sweden to give them Estonia in exchange for help in the war against Russia. The Swedes though thought differently; and the fact that in 1600 Sigismund got dethroned by his brother, Charles IX, made matters even worse.
Turns out Charles IX was a pretty bad king. You'd think an usurper would try to settle things internally before attempting to carry out an aggressive foreign policy; instead, he wages war against Poland, and gets soundly defeated in 1605 and in 1610; not only, he manages to open a second front by repeatedly provoking Denmark, whose nobility, despite this being the perfect chance to strike at Sweden, wasn't looking for war as that would have led to a reinforcement of Christian IV's authority. Internally, matters weren't better: Sigismund was a catholic, so Lutheran Sweden kinda appreciated the fact that he was no longer their king; but at the same time, some of the high nobility were bound by oaths to their rightful ruler, and some had relatives that followed Sigismund to Poland. Charles decided to act brutally, executing four of the noblemen still tied to his brother, alienating the noblity's favor; he wasn't liked by the clergy as well because they suspected him of being a crypto-calvinist (Lutherans hated Calvinists even more than Catholics, funnily enough; this also part of the reason why the Habsburg went undefeated in the Thirty Years' War until the Swedes made their appearence) and the peasants grew tired of his continous summonings of the Diet and his threats of abdication.
Jesus that was long. I'll try to shorten up the rest, if you want more details, I'll be happy to provide them.
In 1611, Charles IX dies; not even seventeen years old, Gustavus Adolphus had to deal with a constitutional crisis (that, not going to deep into details, was solved quickly) and with a war on three fronts - Russia was under Polish influence at the time: he deals with the war with Denmark quickly but costly, not losing any territories but paying them a huge indemnity, and he manages to defeat and push away Russian forces from the Baltic Sea in 1617. The war with Sigismund and Poland, however, lasts a lot more, as Gustavus, more than actually conquering land, wanted Sigismund to drop his (rightful) claims on the swedish throne. The war ended in 1629, with the intervention of Richelieu's envoy. But what was an emissary of Richelieus doing in Poland, in 1629? The answer is simple: at the moment, the Thirty Years' War was going badly for the protestant princes. And France could not allow the Habsburg to win that war: it would have greatly reinforced their authority and put a serious threat to France's attempts at continental haegemony. So Richelieu needed Gustavus Adolphus to stop fighting in Poland and bring his men to Germany; to convince him further, France agreed to pay Sweden a hefty amount of money yearly (can't recall the exact amount right now; I think it was 400.000 tallers? Anyway, a lot) to help pay the expenses. This wasn't actually enough to cover them whole, but it helped a lot easing the situation of economical distress that Sweden was suffering at the time.
So with French support, Gustavus Adolphus took part in the Thiry Year's War; as you probably know if you listen to the right kind of music, he was able to defeat the imperial army, not once, but three times, at Breitenfield, Rain, and Lutzen, where he found his death, in 1632. Since Christina, the heiress to the throne, was still too young, chancellor Oxenstierna took command of the army; but the alliance with the German protestant princes was struggling; at Nordlingen, the imperial army scored a great victory, that lead to the peace of Praga in 1635, which put an end to the German civil war part of the war. The direct intervention (no longer just financially helping the Empire's enemies) of France, however, rekindled the conflict, although at this point it had lost most of its religious component.
At the end of the conflict, in 1648, Sweden obtained the regions of Pomerania and Wismar, that granted them a seat in the Imperial Diet; they were now one of the major players on the European chessboard; but their power wasn't based on a solid foundation, as the second half of the Seventeenth century would show.
Phew. Got a bit rushed there at the end but I hope I answered your question. Feel free to ask questions if you need more in-depth explanations.
The sources I based this on are:
Gustavus Adolphus and the rise of Sweden, by Michael Roberts, an excellent book on the argument, if a bit old. Also Roberts is kind of a fanboy when it comes to Gustavus, so keep that in mind!
The Thirty Years' War, by Geoffrey Parker, for the details on Sweden's role in the Thirty Year's War and its relations with its German allies and France.
The Swedish Imperial Experience, by Michael Roberts once again; this doesn't actually talk about what I said in my post, but it's an excellent read if you're interested on how Sweden built, mantained, and then lost its empire. It kinda skips on the events though.