Use the adjective unexpected to describe something that takes you by surprise. An unexpected knock on your front door might make you jump.
When you don't anticipate something, and have no clue that it's coming, you can call it unexpected. A successful surprise party is always unexpected, and an unexpected visitor can be exciting or inconvenient, depending on who it is. If you expect an event, you know it's going to occur, but if it's unexpected, it seems to come from nowhere. The Latin root is expectare, "await, look out for, desire, or hope."