In the early days of Mobius, there was no need nor want for any police force as citizens were always at war. Around 600 or so years ago, they began to live together peacefully and knew no squabbles. The appearance of Doctor Robotnik and his subsequent takeover of the planet lead to him instating his Trooper forces as police of sorts, ensuring that the residents of Mobius didn't break his laws and were sure not to fall out of line. This policing method appeared brutal, yet efficient at the same time. There weren't many documented cases of small crimes; perhaps this was down to fear of the consequences laid down by the Badnik armies, or that the citizens pulled together against a much stronger enemy which vanquished any desire to harm each other. Whichever reason, the Troopers and all other Badniks were eventually foiled due to the electromagnetic pulse of Issue 100, completely decimating this branch of peace-keeping.
Following a quick brush with global elections, the idea of Zone Leaders was (largely off-the-cuff) devised by Sonic in order to avoid the same problem of dictatorship. With one person in charge of each Zone, these important officials needed some sort of 'army' to defend their new provinces. As such, many Zones had police forces, all of which varied depending on the size of the Zone (and, obviously, the artist and writer of individual stories). Although it was down to the police to apprehend criminals in their jurisdiction, it was often down to Sonic (or, more commonly, Tails), to tackle the crooks first and leave the locking up to the actual authorities. Many officers in one-shot stories (particularly in ones illustrated by Mick McMahon) resembled Russian secret police, their stereotypes coming out with their gruff demeanour and long trenchcoats adorned with a large red star.
In Sonic the Comic Online, modern policing is often represented by the police force of the Metropolis Zone. Led by bumbling Police Chief Bodger, the service was a much more complete one, far more advanced and together than any police representitives thus far. As a unit, they were often more capable of handling tough enemies, with the Freedom Fighters simply in attendance, or for back-up, many times. This was first seen in the print STC, when tackling the Chaos monster, but, more recently, grappeling with huge Uberniks as Tails looks on, nonplussed. Unfortunately, their efficiency has also led to the inadequacy of Sonic.
Other police services shown in STC-O include the Starlight Zone Police Department, which includes highly trained tactical units.
The police of the United States, who unlike the UK's police go around armed with guns, have appeared in both Larson's Revenge and the Streets of Rage series. In the latter, at least in "The City", the police are basically another street gang, massively corrupt and willing to murder the few honest policemen. Axel Stone, Blaze Fielding, and Max Hatchet left the police so they could fight crime better as vigilantes.