Ask yourself this, if you need more help deciding on whether or not to do it.
Does the company you're applying for have an HR department and/or hiring department? If so, is it in house? If yes, then if they're worth what they get paid, they have procedures and policies in place when it comes to dealing with Personal Information, so in that case, yes, you'll probably be fine giving it to them.
If their whole in house hiring procedure is a manager in an office with papers on various stacks and piles, and/or in no immediately identifiable sane configuration, then you may want to hold off on giving it.