Taking advantage of the colonial game incredibly early on was a huge factor in them becoming a major power. This was mostly due to their large-scale mines shipping silver, copper, gold back to Europe, which of course, made them incredibly rich, and more eager to continue building up a navy of hauling the precious metals back, defending them, etc.

Additionally, a series of excellently timed successions occurred. The inheritance of Aragon and Naples, for instance, and the wars that followed for other portions of Italy, were instrumental to setting up Spanish prowess on the land as well as at sea.

Unfortunately, over time, rampant inflation, and huge manpower drainage due to wars, plagues, and famines, left much of continental Spain in dire economic straits. This was reflected in both their military, and their colonial pursuits, leading to more autonomy, a less powerful navy and army, huge number of loans, etc. The real, final nail in the coffin would have to be the accession of Charles II to the throne. He was mentally stunted, physically disabled, and infertile. This not only led to Spain becoming more and more apprehensive about him not producing an heir, but his lackluster leadership allowed quite a large amount of corruption to flourish under his reign. Also, the Spanish army was sort of becoming outdated, sticking to the tercio when it was clear that it wasn't working out is a good example. He just couldn't funcitonally push reforms for anything really. Together, this wouldn't be that bad if it were for a few years or something, but he reigned for nearly forty.

Silver mining in the Spanish colonies was extremely valuable and brought in massive revenues for the Spanish crown. But this didn't come from shipping it to Europe, a relatively small amount actually went back to Europe. The majority of Spanish silver mined in the new world was sent to Manilla in the Philippines and then on to China. Under the Ming dynasty China had a brief experiment with a paper currency and their economy suffered from it, so they switched to a silver standard. This meant one of the largest empire in the world in terms of people and economies suddenly needed massive amounts of silver to base their currency on. Silver went through a massive inflation where its buying power was hugely increased within China. Europeans (and Japan) took advantage, shipping well over 100,000 tonnes of silver a year to China. This gave the Spanish a large influx of mainly Chinese gold, but probably some trade goods as well. Taking advantage of this the Spanish had a massive treasury from which to draw. Another major factor was their size, by the time the Hapsburg family took the Spanish throne they controlled a massive amount of European (Spain, Portugal, Naples, Austria, the Dutch lowlands, among others) and overseas territory to draw taxes and manpower from. They were able to become the most dominant power because they were so wealthy and large.

I can see two large reasons for why they could not sustain this position. Firstly, economically Spain ruined itself. They used the majority of their wealth to fight a series of long, bloody and expensive wars that didn't really get them anywhere. The Hapsburg dynasty saw themselves as this Catholic protector and as a major source of Christian power, they made it their duty to go out and conquer to spread the Catholic faith. For example their attitude in the new world was not one of official subjugation or persecution of the native peoples, but one of conversion. Las Casas saw the king of Spain as failing in his duty as a Christian sovereign by letting the native populations be slaughtered rather than converted. So you have this empire extending itself all over the world fighting in the name of the Catholic faith against Protestants and Muslims in religious conflict and other wars, all this took a tole on them finically. Also, after a time the massive silver production of the new world solved the bullion crisis of the old world. The silver prices in China finally stabilized and the buying power of silver was brought down quite substantially. So we have an empire in debt from war that has lost one of its major sources of income. There are other factors at work for sure in the fall of Spain, but the economic factors are really one of the things that hits them hardest.

Dennis O. Flynn and Aruturo Giraldez, "Born With a Silver Spoon: the Origins of World Trade in 1571" Journal of World History This is where I got most of the information on the silver trade if you want to do further reading.

While the other answers so far aren't necessarily wrong, they do leave out some important aspects of the rise of the Spanish Empire. It's true that the Spanish empire was early to the colonial game, but this leaves out the fact that the Spanish Empire - which we refer to as the Habsburg empire at that point - was already a dominant force in Europe.

The story of the Spanish empire actually starts much earlier than that in several areas of Europe. While you could look at a map of Europe during the Middle Ages and see a patchwork of small duchies, kingdoms and fiefdoms, this began to change towards the end of the Middle Ages and the start of the Early Modern Period. There was a certain trend towards centralisation - in that single rulers began to rule over larger and larger territories but also in that the power within those territories would increasingly be centralised in one spot. We see this trend in several areas of Europe, most importantly for this question in the Iberian peninsula, the Low Countries and in Austria. This trend took on many forms: outright conquest, inheritance or by simply buying certain lands. In Austria, Frederick III of the house of Habsburg united the Austrian provinces (Upper, Inner and Lower, I believe) becoming both Archduke of Austria and Holy Roman Emperor. Most of the Low Countries, meanwhile, were united within the Burgundian Netherlands. In Spain, the Reconquista could be seen as part of this trend, but also the coming together of Castilla, Leon and Aragon - and eventually, these lands would come together under the dual monarchy of Isabella I of Castille and Ferdinand II of Aragon.

Now, here's where they come together. The Burgundian Netherlands and the Burgundian dynasty came to an abrupt halt when Charles the Bold died in battle in 1477. While he did have an heir, Mary of Burgundy couldn't withstand the pressure of the French crown and turned to Frederick III of Austria's son for help. This son, Maximilian I, married Mary and thus became ruler of both the Burgundian Netherlands (though Burgundy proper was lost to France) and of Austria. Maximilian's son, the short-lived Philip I, married the daughter of Isabella I of Castille and Ferdinand II of Aragon, Joanna the Mad. Their son would thus inherit Habsburg Austria, the Low Countries, Castille and Aragon and some lands in Italy. His name was Charles V and during his reign the Habsburg Empire reached its rather impressive peak. After his abdication, however, the empire was split into two - the Austrian Habsburg empire and the Spanish Empire (which also included the Low Countries, parts of Italy and the colonies).

Now, if we were to put the colonial ventures in that timeline, you'd see that the whole affair only comes into play late in the game. Isabella I was the one that sponsored Columbus' journeys. Charles V was the one who first started investing in setting up actual colonies. Philip II was the one who could enjoy the benefits of colonies from the start of his reign to its end. So essentially, early entry into the colonial game itself, while important, isn't the sole reason for the rise of the Spanish empire. More important in funding the rise of the Empire was the fact that it controlled or tried to control some of the wealthiest areas of Europe at that time. The various Austrian dukes I mentioned tried to control Northern Italy, which was insanely wealthy. The Low Countries were probably even wealthier at that period of time, with the cities of Bruges, Antwerp and Amsterdam at one point or the other being vital parts of the European trade routes.

There's more to it, but I just wanted to point out that it's not just colonialism that helped give rise to the Spanish Empire and give some context for their rise as well.