The Pikemans pot, the morion was prescribed for all pikemen at least until the end of the 17th century. Indeed when armour was dropping out of fashion, it was only the helmet that seemed to stay on the infantry.
There were many, many types of helmet, this sprue gives just a few of the types that were worn. Earlier helmets e.g. cabaset would also be available. Musketeers were also expected to wear a helmet or ‘Head-piece’ as they were called right up to the start of the English Civil War and can be seen in Continental armies fighting the 30 years war.