Absolutely, by default you should close a stream.
A stream is a very generic API; the whole point is that it represents a stream of data without requiring the consumer of that data to understand where the data is coming from.
Closing a stream which does not need closing has no cost; failing to close a stream which needs closing may cause serious issues. How sure are you that the code you are writing, which currently consumes a stream of data which does not require closing, will never be repurposed to consume a different type of stream that does require closing?
I just finished refactoring a ton of code which used to use an in-memory database to use a SQL back-end instead. The code in question used streams a lot, and for good reason. Encapsulating a JDBC result set in a stream meant that I could (...I thought) achieve my goal quite easily. But... my new stream encapsulated a resource that required closing, whereas the old stream did not. Because the original developer (in this case me, I'm kicking myself) did not close the streams, much tedious debugging was required.