How long do I have to keep monthly statements if I've paid by check or credit card and there's no dispute? - I'm drowning in paper! Thanks!

I guess I'm really asking if there is a reason to save these statements more than a month or two after they've been paid... thanks.

The title of your post is "saving statement for tax purposes" - if in fact there are transactions on these statements that have tax implications then you want to save them for preparing your taxes next year, and then you should keep them with your tax records for at least 3 years after that. However, if there really are no tax implications, in my opinion you simply keep statements until the next one arives and you can check that there are no errors or charges to dispute.