People of a certain generation are used to keeping every bill and receipt they've ever received, while it would never even occur to a younger generation to do so. The best practice lies somewhere in between.
I always encourage my clients to only keep paper copies of documents that need to be produced in original form, think birth certificates, passports, visas, vaccination cards, etc. All other documents can be scanned and digitally uploaded to an external hard drive or cloud service and then shredded or simply thrown out. Additionally, documents like bank statements, medical bills and water bills can often be reproduced directly from your account with the service provider negating the need to keep them at all.
Below are general guidelines for the length of time you should keep documents (in original or digital form):
Tax Returns: 10 years
Insurance and Medical Records: 5 years
Utility Bills and Pay Stubs: 1 year
Credit Card Receipts: only until you've reconciled your statement and have ensured there are no discrepancies.
Determine what documents you want hard copies of, and then decide on a digital storage system that you are comfortable with. Any documents with personal identifying information, beyond your name and address, should be shredded. Everything else can be recycled or tossed in the trash. You'll be surprised how much space you free up by doing a document dump!