Is there anything worth believing that could not hold up to Scientific scrutiny?

If so, can you give an example of something that is worth believing despite the fact that it could not be demonstrated Scientifically?

Lately, I’ve had something in the back of my mind and I don’t know how to articulate it as yet. I know there are things in life that we won’t ever put through an all out Scientific study either because we don’t really have the time or because we simply neglect to consider the merits.

Feel free to list things that might fit this bill. Even if you aren’t sure whether they can or can’t somehow be tested Scientifically. What I propose we do, is discuss some of the items we list and figure out how we could possibly test some statements for Scientific validity and try to isolate the kinds of statements that we aren’t able to imagine a practical way to study and validate from the Science perspective.

So, what kinds of things can we possibly study Scientifically and what kinds of things can’t we study Scientifically? List some examples for discussion.

Now, of the things in the second class, what would be the value in believing them to be true if it doesn’t seem possible that they could ever be measured or studied Scientifically?