I'd encourage you to keep bank statements for up to 7 years as I believe that is the period that you're subject to audit. If you're audited, you could be called on to support every deductions and deposit. If this is a problem, I encourage you to save images that you can download online...or convert your hard copy to a .pdf format through fax...but if you do this, you'll also need a backup plan.

EOBs? You're safe...frankly, I don't have a need to keep them beyond one year unless they assist in evidencing a big tax deduction.

I image everything I can...so I can trash the paper.