I'd always thought of the Chinese Empire's decline as being a simple case of stagnation while other powers grew in prominence and eclipsed it. But my experience of studying history has shown that such changes are never quite as straightforward as they appear. What were the processes that caused China to be in such a poor state relative to the centuries of practically proverbial supremacy it had had in the past?
First off, it's important to realize that the multiple dynasties over the period of the Chinese Empire came and went. While it is oversimplification to say all dynasties collapsed because "X or Y", many did succumb due to political corruption and rebellions.
The Qing Dynasty arguably began it's downturn during British occupancy. Britain wanted the handful of goods that China was able to produce (tea, silk, opium), however there was a few problems. First off China only dealt in silver while Britain was on the gold standard. Secondly, China was not interested in making the trade of opium legal. This led to the Opium Wars in which Britain France and Russia took total control of Chinese trade. This essentially was the beginning of the end for the Qing.
Multiple rebellions (Taiping, Boxer) were beginning to rise during the later 19th century when China was under the control of the European powers. Most prominently, Sun Yatsen rose to power and began to influence China's development into modern times. Meanwhile, Empress Dowager Cixi resisted change leading to the Hundred Days of Reform. This eventually led to the Xinhai revolution where Sun Yatsen was able to take power as well as former Qing generals (notably Yuan Shikai) that created a new period of warlords who controlled various sections of China. Ironically even though it was the end of Chinese imperialism, the division of powers created another period of warlord-ism.
Intellectual failure. The academic path to success, fame, and fortune in Imperial China was through the state examination system, which primarily tested mastery of classical philosophy and literature. There was no science/engineering/management track. The brightest scholars of Ming and Qing China focused their minds on competing with each other for government positions rather than keeping up with Western science, technology, and thought. Lack of immediate external military and economic threats enabled China to maintain this intellectual isolation until the 19th century, by which point it was almost impossible to "catch up" to the west.
I've heard the argument in Guns Germs and Steel that the Hongxi Emperor stopped all the exploration and with less contact with other cultures a culture can stagnate.
This argument is that China's downfall is hubris. They want to be homogeneous and they sort of stopped trading. In other places the countries competed with each other and that brought about more successful ways to run a country.