It is completely possible in Ukraine to bribe the police and avoid a drink driving or other serious motoring conviction.
In our personal experience we have never been asked to pay a bribe when no traffic offence has been committed.
We personally consider it much better to leave our passports in a safe place than to routinely carry it in person and risk losing them. If you have committed an offence they will usually give you the option of going down the official route or paying a bribe and going on your way.
Having said that, official guidance from both the US and British embassies states that visitors should carry their passports with them at all times and keep copies in case of loss or theft. They are notoriously corrupt, though you should only come into contact with them if you are driving. Paying the bribe is cheaper than the official fine and less hassle.
In general, Kiev is as safe as most Western European countries.
Organized crime does exist, but unless you’re coming to Kiev to open a chain of casinos the mafias are extremely unlikely to take an interest in you.
Street scams are frequently reported by other websites and government agencies as being fairly commonplace in Kiev.
We personally doubt whether they are as widespread as made out.
Taxi scams are also common but can easily be avoided.
There are, however, reports of racist attacks on those of African and Middle Eastern appearance.
Under Ukrainian law you are supposed to carry your passport with you at all times.
A bogus policeman then appears and demands to see the tourist’s wallet.
At some point during the inspection he secretly pockets some cash, before handing it back and informing the tourist he is innocent and can go on his way. But quite frankly, the idea of large numbers of fake police frequenting Kiev’s tourist hotspots is preposterous.