Short Answer - Yes. For instance, one of the traditional arms of the Swiss Guard (still in use in the Vatican, for example) is the halberd - a mix of a pike/spear/axe (which someone mentioned) which some carry (mainly for show) to this day.

Long Answer - it depends when and where we're talking. I'm guessing you're wondering about the practicability of using a weapon such as a spear for inevitable close range combat that would arise in a street patrol. Yes, long spears were the primary weapon used by foot soldiers for many civilizations throughout history, but this type (think 20 ft Greek/Macedonian phalanx-length spears) would not have been used for patrols or bodyguards. The ones the Unsullied use, however, would certainly by used by several groups throughout history. Spears of this type are much cheaper to make and mass produce (since typically only the spear head need be iron) than say a sword or other close range weapon. And many soldiers would have been trained to use this shorter spear in close combat. Again, this depends when and where we're talking, and it also depends how much one was willing to spend on the foot patrol. Guards in the Roman Empire, for instance, would likely carry a javelin (shorter, throwing spear), but, more importantly for close combat, would also be equipped with a short sword. So mainly the factors would center around the money spent on your guards, the technology of the time, and the typical weapon carried by a soldier in a specific city. Sorry to be broad, feel free to ask anything more specifically.

I guess they'd be good for riot control, but wouldn't a sword be better for fighting in close quarters?

Spears are great for crowd control, because they keep the crowd far away. However you are correct in saying that a short sword or a long dagger would be much better in the tight side streets of Meereen. Maybe they never expect to actually have to use their weapons and were carrying them for psychological effect.

Did any civilisations use spears? What are the more common patrol weapons in medieval Europe?

Spears (or other long and pointy weapons) were pretty much the standard for almost every soldier or mercenary in all of history.

Nearly every civilization in human history utilized spears at one point, and many of them used them prominently as a tool for many occasions. Armies had people carrying large pikes that ranged from 6 ft long to over 20 ft long on the battlefield. Guards in cities carried all sorts of spear like weapons, including halberds and billhooks, in addition to several types of spears. Throwing spears were common as a hunting tool in almost every part of the world, but many civilizations also used them as weapons on the battlefield as well.

If you have any specific questions regarding my answer, feel free to ask.