Supposing around 1% of the world population has some kind of superpower, about 70-80 million people on earth, and only 1% of those have taken to superherodom, what items would be worth the risk of stealing? In a city full of heroes, what could a non-powered thief steal that would go under the radar so to speak, or would be easy enough for it to be stolen and yet the thief could escape or avoid pursuit, so as to become a commonplace event?
Exactly the same things as nowadays, for several reasons:
The risk profile doesn’t really change. The end result of being caught stealing should still be arrest, not murder-by-supercop. Sure, a supercop has extra skills they can use to arrest you, but the end result is still trial and jail, and evidence collected by (for example) a person with a super sense of smell will have to somehow be verified in court. If the superhero is a vigilante then they themselves are a criminal and any evidence provided is extremely suspect. It’s not like Superheroes suddenly have carte-Blanche to go around murdering people they suspect of crime, right? Right??
Theft relies mostly on not getting caught (either stealing or moving the goods). Unless your heroes all have skills that are useful for detecting people trying to engage in criminal enterprise (like telepathy, or Crimey-sense) the presence of a super powered police force isn’t going to alter whether they can successfully lift and shift goods. For low value items and crimes of opportunity all that changes is who puts the handcuffs on if you get found out. For high value items and heists it simply adds another kind of security you need to plan around.
Those driven to crime are usually not doing it for fun. A person desperate enough to purse snatch will still purse snatch even if they might then be pursued by a super cop. A person stealing high end jewellery will still have debts to pay that they need the gems for. Compulsive shoplifters won’t suddenly be cured of their compulsions because they might get caught by Spidercop.
And finally: Your regular criminals will still be dealing with regular cops. The superheroes will be needed to deal with the supervillains. In the same way that armed response officers (in countries that don’t regularly arm police officers) are reserved for situations where they’re really needed, you can expect super-officers to only be deployed for super-crimes.
After all: Why waste your Bulletproof Sergeant ploughing through reports of lawnmowers going missing from garages in the suburbs? Shouldn’t he be off stopping Doctor Maniacal from detonating that bomb under city hall?
More cautious, little difference
Criminality for your question can be sorted in two very broad strokes. Crimes where they are spotted or can be tracked instantly and those they are not. The ones that you are not are the exact same as before. Burglary will allow them to steal anything if they aren't caught. Even if they are they might still be able to intimidate or use violence against the superhero. A person that can shoot lightning can still be shot, hit with a fist or simply be scared of unknown people with possible powers in the house. Besides, excessive violence isn't something that most people are willing to do. What if in such a stressful situation he electrocutes the criminal(s) or stops their heart?
Other crimes are much of the same. Cycling past and snatching a phone or bag might be more dangerous now, but in many cases it might still work. Threatening or even just stabbing or shooting someone can do the trick. Drugging people at a bar and stealing when they pass out outside or the like are still viable. But most is also pretty theft. That means the repercussions are also low. People know you can't use too much force if someone steals a wallet without violence. At least in civilised countries. They might have to pay a fine, do a short term of labour or in bad cases prison and they are at it again.
Finally theres the crimes of threat. A hostage situation. The law often has more power and skill to bear, but the threat of losing life is enough to keep them at bay. Same can be said in a city of superheroes.
The only thing that has happened is that there is an increased risk. People are more likely to take a cautious approach, sometimes resulting in more violence as a preemptive strike to neutralise a potential threat.
As long as crime pays, which likely it still will, crime will happen.
A super hero(ine)'s heart
I come from a place where the police usually does not catch thieves because they get a share of the loot. Doesn't matter the scale of the theft, whether it is a purse or a bank vault.
If you get a super powered being on your side, then you can continue doing crime with impunity as now you've got a shield against other super powered beings. Moreover, since supers are rare, you might not have to worry much about super heroes - but your super lover will fedinitely keep the police at bay.
Just about anything unless the superheroes have organised themselves in a lawful non-vigilante way. What would we call such a superhero organization? Well you could always call it a "police force".
That would mean that any crime is basically as detectable and preventable as today, give or take a few superheroes that have ways to detect crime that current technology can't. Most of the time the threat of being shot or potentially killed by police forces wouldn't really surpass what a superhero is willing to do, able to do and allowed to do unless you start counting anti-heroes, who work outside the law and wouldn't be able to rely on a police network to detect crime. You might argue "my hero will use a police scanner to detect what and where is happening!" But that still means that you need a way to get there and not get caught as soon-to-be-known vigilante while the police is better spread out to deal with it and now reinforced by superheroes.
Trophies from supers.
Some non-supers feel like they are second class because they don't have powers. Secret clubs of these folks make themselves feel worthy by stealing stuff from supers - the hero ones but also civilian supers and supervillains too. Bragging points accrue according to the dangerousness of the stealing feat and also the trophy itself. These thieves have trophy rooms where they assemble, brag, smoke weed and scheme up the next theft.
For example, stealing underwear from that hot blue supervillain that freezes people would be a very bragworthy deed because she is scary mean and kills people for fun. Stealing a BatBelt from Batman would also be bragworthy but maybe less dangerous because he is unlikely to kill you for fun but also probably is harder to steal from. Stealing the rubber toad off the dashboard of the guy with supersmell powers is just sort of for completeness sake (and the thief left a rubber dinosaur in its place because supersmell guy is a good guy). Stealing a box of Cheezits from a guy who has the power to really eat a lot of Cheezits is more just funny, because people doubt it is really a superpower until they see video.
Finaical crimes/things that can be done mostly online. Do your superheroes have any abilities to help track down financial fraud or tax evasion? How about a company director cooking the books and stealing from thier investors? Or people writing malware/viruses to steal banking details or just extort people with ransomware.
If they want to steal, they will
If someone wants to steal something, the only deciding factor is their sheer determination. Having superheroes in the setting is just another obstacle to work around rather than a deterrent that would simply cause lesser crime to evaporate overnight. The human race is defined by adapting to everything the world throws at it, and whatever the human race throws at itself in the meantime and that's how things will stay.