The problem occurred after I had added Groovy Unit Testing .jar to my project (it is sole activity I suppose which could 'damage' my Intellij but it is quite likely that the reason is something else because the problem is global - it appears in all projects).
For example I get message like this:
but after I press Alt+Enter nothing happen.
If I append another keyboard shortcut for "show intention actions" it doesn't work either. However if I append Alt+Enter with another action then that another action works properly using this shortcut.
It is also interesting that shortcut Alt+Enter is reserved not only for action "show intention actions", but if I remove another associations it still doesn't work.
Every intentions in Intellij are enabled and power save mode is disabled.
I have read IntelliJ, Alt+Enter doesnt work Auto errors detection in IntelliJ IDEA but it doesn't solve my problem.