A surprise (as a noun) is something that you weren't expecting, but, in general, was planned by somebody else. Your examples in bold all match this description, like a surprise party, suprise trip, or surprise gift.
However, the other examples, such as the car accident or the power going out, were things that nobody planned, and are usually called accidents or mistakes.
It's possible to "be surprised" (as an adjective) by almost anything, planned, unplanned, or whatever. I can be surprised when the power goes out, even though nobody planned it for me. "And then the power went out. Yeah, that was a surprise!"
Actually, I guess a surprise can be anything that surprises you.
"Don't you look so surprised!
Happy Birthday, f***er!
You blow that candle out
We're gonna kick you, kick you!"
-Faith No More, Gentle Art of Making Enemies