I have a fairly dystopian dictatorship with a police state.
There are two ideologies amongst the population.
The first - the more mainstream - in general support the rulers and the police and the wish to maintain the status quo.
But there is a second, smaller, rebellious part of society who wants to overthrow the government and are very much anti-police, believing them to be hard-line freedom-haters. These are not criminals and certainly not violent, but they are not happy with the current state of things.
But I've a problem. There is very little or almost no actual person-on-person type crime in this society (robbery, violence, etc.), and in fact, the police's main function is putting down the rebellious crowd - arresting people spreading anti-government propaganda and the rebellious leaders, breaking up meetings, hijacking people's individual initiatives to hand over to the government, and the like.
So how do I justify the pro-government people's love of the police? I can't exactly show them protecting the ordinary citizens from muggers, wiping out organised crime, solving horrific murders, ridding the town of drug-dealers, rescuing children from child-porn gangs, etc, because there is none of that stuff.
Thanks for all the great answers, but judging by some of the comments, etc. I realise I probably left out a lot of potentially useful details:
First of all this is a land of very scarce resources, causing poverty throughout the society. However, the government, and pro-government people believe that they are making the best of a bad situation and that the rebels will cause the structures that are there to fall apart, resulting in starvation and the potential destruction or decimation of the society.
The police are relatively "evil" by modern standards - using excessive force, arresting people for the slightest anti-government sentiments (think "thoughtcrime"), confiscating things from individuals "for the benefit of society" sort of communist style (though it usually just ends up in the hands of the high ranking officials) - which is especially jarring because resources are very scarce in this setting, enforcing what we would call slavery (in one case hauling someone into work despite him being too sick). They are also intimidating in appearance.
They have every reason to be hated, and in my personal opinion the best opinion someone could have would be indifference (if they weren't personally affected or didn't witness their evils), but in this scenario, I want the majority of the populace to actually like them, and, for example, be horrified when one of them is attacked in an uncharacteristic moment of violence by one of the rebels.
The low crime is not, in fact, thanks to the police (though I understand propaganda could be used to make it look like it was), it is in the nature of the people not to commit crime, and in theory, no crime prevention would be required at all in this society. The police were actually introduced by the dictator to help him enforce his will rather than prevent crime.