Receipts for big ticket items should be kept as long as you own the item for insurance purposes.
As an income tax preparer, I know that IRS says you need to keep your tax records for the 3 years prior to the current year. That applies to the other records you refer to. If the receipts or cancelled checks apply to something you have reported on your taxes, keep them with your copy of that return for at least 3 years beyond the date you filed the return. For example, checks written for charity, real estate or personal property taxes, business expenses you have claimed. No need to keep the cancelled checks for your house payments or the like, your Form 1098 is sufficient for tax records.
The only other reason you would need to keep copies of paid bills is if you are trying to track your usage. Otherwise, you may as well get that shredder warmed up--you've got plenty of "food" for it!