The city, especially its central part, is quite safe - robbery here is impossible in principle, only homeless people or former compatriots can steal from you. But fights are not uncommon in Helsinki, especially on Friday nights - try to stay away from drinking establishments at this time.
To protect yourself from misunderstanding and conflicts on the street, respect other people's personal space when addressing Finns - excessive emotionality is not appreciated here, and an innocent pat on the shoulder can be perceived as an insult.
If you have any problems, contact Helsinki Help, a service for tourists. You can recognize its representatives by their bright green T-shirts - from June to August young people patrol the center in pairs.