I mean, at the beginning it was just Bohemia and Austria. What caused nearly every European power to involve itself in the war?
There are much better guys around, but I'll take a shot at this one.
Two main reasons jump to my mind. Firstly, the war could be seen as an attempt to reaffirm a Habsburg hegemony over Germany, hence involving Austria and to a lesser extent Spain. That's political.
Secondly, it was fought on religious grounds, with the hardline Catholics (Jesuits, Spanish, Austrians) attempting to suppress what they saw as the Lutheran heresy.
Others like Denmark and Sweden intervened also on religious grounds, although Christian of Denmark may have had territory on the mind as well.France funded the Swedes and later got directly involved in an attempt to weaken the Habsburgs and maintain a balance of power in Europe and improve France's relative position.
Source: C.V. Wedgwood 'The Thirty Years' War'
This is a very good question, and to fully understand how the 30YW grew to become a really great war, we should consider its development.
Peace of Augsburg (1555)
Charles V the HRE emperor, Archduke of Austria, and King of Spanish kingdoms/crowns (and Italian lands, and Duke of Burgundy, and of the Low Countries, etc.) was very much a traveling monarch, visiting his various possessions in Europe throughout his reign. His brother Ferdinand ruled the German lands and titles as Charles' representative. It is in this era that the Protestant Lutheran reformation began. In addition to representing Charles as HRE emperor, Ferdinand was also king of Bohemia and Hungary, and of Croatia. This meant that he had to deal with Ottoman expansion into south eastern Europe.
The Augsburg treaty was very much a compromise. (1) Each ruler determines the religion of his realm, either Catholic or Lutheran. (2) If a prelate of an ecclesiastic state was to convert from Catholicism, then he has to give up his post. (3) Due to his need for military support, Ferdinand added a third secret clause giving exemption to knights and some cities from religious uniformity in that realm, under some circumstances.
More importantly, this treaty left large "loopholes", tested soon after in the Cologne War in 1583. The Prince-Bishop of Koln, which held electoral power, wanted to convert to Calvinism, and while he didn't force his subjects to convert with him, he gave Calvinists equal rights as Catholics. Further, he wanted to keep his ecclesiastical post and electoral power. Finally, he wanted to marry, thus threatening the ecclesiastical nature of his realm. This war saw the HRE emperor, Bavaria, Spain, and several other powers converge to win against the Prince-Bishop and his allies.
Dutch Rebellion and the Thirty Years' War
I will only cover this minimally. When Charles V abdicated, he preserved Spain along with his possessions in the Burgundy and the Low Countries, and in Italy, to be inherited by his son Philip II. His brother Ferdinand became HRE emperor and archduke of Austria, and lands in Germany in addition to Hungary, Croatia, etc.
The Dutch rebelled was partly due to religion, including Calvinism, Anabaptism, etc. which were not included in the Peace of Augsburg. In order to send troops from Spain to the Netherlands, the Spanish had to use the Spanish road from Italy to Switzerland to Franche-Comté and Palatine to Luxembourg to Brussels.
Remember that the Spanish took part in the Cologne War? Yep, Koln is right there on the Spanish Road.
Bohemian Revolt
HRE Emperor and King of Bohemia Rudolf II was a weak ruler, and to bolster Bohemian support in his conflict with the Ottomans, he granted special religious liberty in Bohemia. His successor Mattias followed the same lines. However, his successor Ferdinand II was a staunch Catholic and wanted to reverse these dispensations. As a result, the Bohemians rebelled. To garner support, the rebels offered kingship of Bohemia to Calvinist Frederick V, Elector of Palatine. Recall that Palatine was a strategically important area on the Spanish Road. At this point some Protestant parties still remained on the side of the HRE. Saxony intervened on behalf of the HRE against Palatine. Spain sent troops to help the HRE. The result of this is the Battle of White Mountain, where the Protestant League was beaten by the Catholic League under Count of Tilly.
As a result of this, parts of Palatine was given to Catholic nobles, the electorate was given to the Duke of Bavaria.
Danish Phase
Protestant King of Denmark, also Duke of Holstein, felt threatened by Catholic/HRE success in the area, in particular as Tilly's forces pursued remnants of the Palatine / Bohemian forces. He was supported by the Dutch, the French, and the English. To overcome this new threat, the HRE hired Wallenstein, a Bohemian noble, to raise an army and defeat the Danish army. This army, along with Tilly's, did very well in continental Europe although they failed to take Copenhagen due to lack of a fleet.
This new success emboldened the Catholic League to insist that recently converted lands be reverted back to the religious state of the Peace of Augsburg. They also disliked the strength of Wallenstein and asked the HRE to dismiss him.
Swedish period
Swedish king Gustavus Adolphus was alarmed by HRE success, brought his army across the Baltic to invade the continent. With his new style of warfare, using smaller and more agile infantry formations, he turned the table on the Catholics and won a great battle in Breitenfeld, in the end costing Tilly his life. Seeing the danger, Wallenstein was recalled. Wallenstein decided to threaten Sweden's lines of communication, thus setting the stage for the Battle of Lutzen where Sweden won but their king was killed.
At this point, Spain increased her investment in the war, and in the battle of Nordlingen they won against the Protestants.
Summary
Why did the 30YW grow so big? Throughout it, an upset in the balance of power, and entrenched interests, forced current and additional parties to increase their stakes.
Spain became involved due to their strategic interest in the Low Countries. Saxony switched sides due to increasingly religious nature of the war. Bavaria benefited from Palatine's loss, yet in turn suffered from Swedish intervention. Denmark became involved due to the large number of Spanish and HRE troops near Holstein. Sweden was threatened by successes in the northern areas. France wanted to contain the Habsburgs. Speaking of which, I omitted the Southern Netherlands and Pyrenees theaters for brevity.
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