Coming off a post about the most practical weapon, many users said that the Spear was the best candidate, or a variation of it. I found it curious however that the Helberd, which is arguably better in some areas, was not mentioned. Was the Halberd liked and used often? Or was it dropped in favour of simpler weapons?
The halberd is a 14th century weapon designed to be used in formation to defeat heavily armoured infantry and deter cavalry; it's arguably a more complex weapon to use than the spear, which is probably why the commenters suggested that the spear was the most practical weapon. That said, though, halberds had their place alongside spears (and pikes) until the 17th century, so it was clearly afforded a very important place in the military mindset. It has also been used ceremonially up to the modern day.
The answer to your question is, yes, Halberds were widely popular weapons. In the 15th century they seem to primarily be the weapons of the German Lands, including the Swiss Cantons. In the 16th they see somewhat wider use. Note that other nations elsewhere had polearms of their own, with their own names and shapes (Couse, glaive, bill, ronca, guisarme, etc). Unlike the polearms of the D&D players handbook, the names of these weapons wasn't necessarily a strict description of their form, and weapons of the same name could look quite different in different times. For example, a 15th century halberd looks different from a 16th century halberd. If we are speaking about all Polearms, not just halberds, they were among the most common weapons on Western European battlefields in the later 14th and 15th centuries.
Broadly speaking, polearms offered similar advantages. Top spikes allowed them to be somewhat useful as spears, broad blades made them effective chopping weapons, and their back spike (if they had one) provided a potent combination of leverage and concentrated force - making them the best armour-penetrating weapons available to a soldier on foot*. Hammer heads could deliver concussive blows, possibly through armour, and may have served to smash the joints of plate armour. This combination of weapons in one meant that they could fend off cavalry but also effectively attack heavily armoured troops, including armoured infantry. A special polearm to mention is the pollaxe or poleaxe, which was some combination of hammer head, spike, and axe blade. These were sometimes shorter than other polearms, and were used both for war and for competitive and judicial foot combat between men at arms.
The question about whether polearms were discarded for other weapons, such as spears, is an interesting one, because we can see both spears(/pikes) replacing polearms and polearms replacing spears at different times.
In the 14th century, English men at arms (that is to say, knights and those who fought like knights) fighting on foot often used 'Short Lances'. These appear by the hundreds in 14th century inventories of the royal armoury in the Tower of London. However, in the 15th century these are replaced by pollaxes - perhaps because pollaxes are more effective against opponents in full plate armour.
On the other hand, the swiss of the 14th century used the halberd almost exclusively, then adopted the pike in the 15th - around the time they started fighting more outside of the Swiss Cantons proper. I do not know enough about swiss tactics to state the exact cause. However the Swiss continued to use halberdiers in the 16th century. Though 16th century warfare was dominated by pikemen and arquebusiers, halberdiers and other soldiers with polearms continued to be used, such as the landsknecht doppelsoldat. In the 16th century there are a number of halberds used by guards for ceremonial occasions, like the halberds that the Swiss Guards carry today. Though some of these surviving halberds are very slight and not very sturdy, others, such as the halberds of the Trabantean guards of Brunswick, are sturdy and functional weapons - even if they are extravagantly decorated, which shows the survival of the halberd as a weapon into the 16th century.
Sources: Tobias Capwell - Masterpieces of European Arms and Armour at the Wallace Collection
Edge and Paddock - Arms and Armour of the Medieval Knight
*Maces and warhammers are effective but unwieldy for a man on foot to use - they are generally illustrated being used by horsemen, Such as in 'The Battle of San Romano' by Paolo Uccello.
