I was reading the wikipedia article on PIkes and it says that they were used throughout the renaissance (An age with Gunpowder), Through the 17th century (An age where i traditionally just assumed everyone was using muskets and cannons), where used by some nations in the Napoleonic wars, and were used by Spanish police forces up until the 1980s.
Why Pikes? Or Rather, why was a medieval weapon still being used? Does it have to do with the training cost of them or did they serve a larger purpose?
Pikes were very useful for fighting against cavalry prior to the invention of socket bayonets in the 1700's. They are also excellent for fighting in dense/massed formations, since their length enables men standing 2 or 3 ranks back from the front row of an infantry formation to engage targets.
As the Middle-Ages phased into the Renaissance, armies became larger and more centrally organized. The pike was an excellent weapon for these changes because they worked so well in massed formations and were cheap/quick to produce in large numbers. Pikes were actually less common in the middle ages than they were in the Renaissance. In the middle ages more complex pole-arms like glaives, halberds or billhooks were preferred to the pike.
In the 1600's muskets were slow to load and only had very crude "plug bayonets" that could fit into the muzzle. To protect them from cavalry charges musketeers relied on pikemen to cover them. Muskets actually usually outnumbered pikes among infantry by about 2 to 1 though, so arguably pikes weren't THE main weapon, just an important one. As a matter of fact the tactical system of the late 16th and 17th centuries is called "Pike-and-shot" because the pairing of pike and musket armed infantry formations dominated warfare.
Once sturdy "socket-bayonets" were designed muskets could double as effective pole-arms, and the necessity of having large numbers of pikemen to defend musketeers faded rapidly. Pikes lingered on for a while, especially in the armories of small and/or poorer countries. Reports of pikes being used in the Napoleonic era probably mostly refer to the Russians, who had a shortage of muskets when Napoleon invaded.
If you want to see a pretty good movie rendition of pike-and-shot combat that was common in the 17th century the film "Captain Alatriste" starring Viggo Mortensen does a decent job.
The pikes that were occasionally used during the Napoleonic wars as well as the "Joe Brown pikes" used during the US Civil War were around 7-8 feet long, meaning they were closer to a spear or medieval "half-pike" rather than what we think of as a true medieval pike which could be up to 20 feet long. That aside, in an era where bayonet charges were still common there was still reason to believe that soldiers armed with pikes might still be effective. As Governor Brown put it "Hand to hand, the pike has vastly the advantage of the bayonet, and those having the bayonet, which is itself but a crooked pike, with shorter staff, must retreat before it." His argument was that since enemy infantry rarely stood their ground in the face of a bayonet charge they would definitely not stand their ground in against charging pikes.
In George Silver's 1599 "Paradoxes of Defence", he argued that the half-pike or short staff is one of the best weapons for single combat, having the advantage over swords and buckers, two-handed swords, battle axes, and morris pikes. However in massed combat he writes "The morris pike defends the battle from both horse and man, much better than can the short staff. . ."
In the 19th century however, the very long pikes which would dominate during a push of pike were no longer being used by the enemy, so for a theoretical force armed with pikes they would only need their weapons to have slightly more reach than a musket and bayonet.