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. Crimes perpetrated against visitors are generally low level and include pick pocketing and wallet scams.
Acts of mindless drunken violence such as those which commonly occur in British cities are rare. There are, however, increasing reports of racist attacks on those of African and Middle Eastern appearance.
Although the police in Kiev are no angels, they don’t, unlike their counterparts in Moscow, routinely pester foreigners for documents and bribes.