To a certain extent, medieval warfare plays a lot like a game of rock paper scissors, with armies evolving to counter the biggest and nearest threats. To counter the lancers of the feudal kingdoms, many nations arm their soldiers with large sharp pikes, which can form a sharp defensive wall that most cavalry can't reach, or hope to trot over. Pikemen are largely the citizens of the the northern, coastal nations. Cavalry is much too expensive to maintain where the soil can be much more limited. Likewise, because large communities are so close together, it's more important to feed people than horses. The close consolidation of people also pretty much means speed is not as much of a factor. A mobile infantry can probably move from one outpost to another without much trouble. If they can't, there's always the nearby ocean. In fact, the focus on maritime transport pretty much means captains don't want too many knights, as horses on ships pretty much just complicate things.
It's not to say there are no mounted troops in the Republics--a few high ranking officers are cavalry, if for no other reason than to show off. It's just these nations don't particularly engage in feudal warfare, and are more concerned with being on the defensive.
Because most of them are ruled by mercantile families, not warlords, there tend not to be citizens who were born and bred for combat. The city-states will conscript private citizens for service, and these citizens are given relatively simple training and equipment. For Pikemen to be effective, one simply needs a large pool and leaders with an ability to look at the big picture. City-states will even have a very strong municipal guard force, who are generally equipped the same way, and maybe even bear similar uniforms as the infantry.
Interestingly, despite it being feudal in nature, New Jersey relies more on a pikemen force than knights. New Jersey is largely in the same place as the bustling northern cities, with a large population fitting into a relatively small piece of land, as its realm includes counties that had the highest population density in the country. It only has a few major cities and counties, and they're not widely dispersed from each other, so there's very little need for warlords to mount themselves and reconnoiter the countryside. It also has access to the oceans, so it likewise focuses on sending its infantry. However, the Pikemen here are relatively more ornate, especially the guard captains.
Pikemen have also taken root in the highlands of the Appalachian mountains. Here, the people are usually not wealthy enough for mounted knights, nor is it advantageous for the altitudes. Rather, they're large wooden polearms held by clan militias. The mountain fighters are quite different from the other pike-holders, as they're not really uniformed. conscripted armies, but clans bound together by loyalty. Here, pikemen have firm, lightweight wood polearms, which some have even taken to throwing like javelins. Appalachian forts are also known to surround themselves with "pike moat" traps.