I'm pretty diligent about tax records and HSA receipts. Beyond that, very little paper is received or saved. I don't scan, print, or retain anything on a routine basis (physically or electronically) except HSA and tax stuff. A few one-off exceptions:
We have a fire proof box that contains tax records for the last 7 years, all of our wills and related documents, passports, vehicle titles, unused credit/debit cards, SS cards, birth certificates, and other important documents.
My desk in the office has a 2-drawer file cabinet. The upper drawer is current, ongoing stuff and it's kept well organized. Old stuff is regularly purged and shredded. There are folders for health insurance, EOBs, HSA receipts, current year tax documents, a tickler file, car registration and maintenance records, etc.
The lower drawer is less important, less current, and probably needs to be purged a bit... dog shot records, house and car purchase documents, old insurance claim documents, invoices for big purchases/repairs, retirement documents for DW and myself, rental-related documents, and a few tax returns older than 7 years.
Only other thing worth mentioning is that I have 3 small cardboard boxes in my closet. Two of them contain sales tax receipts for a couple recent years that we took the manual sales tax deduction on our federal return rather than using the IRS calculation. The other box contains the first 5-6 years of HSA receipts.