As long as you compare Stockholm to other major cities in Europe you can say that it is safe in Stockholm. So far Stockholm safety levels are similar to London, Paris or Berlin for inhabitants and visitors. There are suburbs you might avoid unless you look for the adventure of meeting gangs who can be fairly aggressive.
Subways during nights are places where you might not go completely alone. Make sure that you have company or that there are other people similar to you going in the same directions.
If you compare the safety of Stockholm now to how Stockholm felt 10 years ago or more you will find that the amount of crimes on the streets have increased quite a bit. Stockholm have many illegal immigrants living anonymously in Stockholm that have to provide for themselves. There are a lot more people with psychological problems around mainly due to the cutting down in care and treatment of such disorders. However there is no way of proving any claims of growing crimes so far as Swedes do not like to keep statistics of negative events. Crime statistics get filtered to show a positive outlook on the current state.
There has been an decline in the number of police on the streets for several years and any given day the police in Stockholm have more to do than they now can handle. If you read the staggering police incident reports it’s easy to feel insecure. But this is nowadays a normal situation all over Europe and the open borders of EU has brought a lot of people also to Sweden who are not part of the society as working taxpayers.
Summary: What is the “true” situation of safety in Stockholm you might ask? The safety of living in Stockholm is probably going in the wrong direction but Stockholm is still considered a safe city similar to other capitals like London, Paris or Berlin.
Be on the lookout for pocket thieves in crowded areas, be as alert as you normally are but do not waste a wonderful experience visiting Stockholm by worrying to much.