Keep for 1 Year

Paycheck Stubs until you get your W-2 in January to check accuracy (You should check your social security earnings record by visiting www.ssa.gov every few years to make sure it is accurate, particularly before destroying W-2s, which would support your case if earnings have been missed).

Bank Statements to confirm your 1099s
Brokerage Statements until you get your annual summary (keep longer for tax purposes if they show a gain or loss)
Receipts for health care bills in case you qualify for a medical deduction (if you do, keep them for 7 years)
Utility bills to track usage (seven years if you deduct home office)

Keep for 4 Years

Supporting documents for your taxes including your W-2s, 1099s, and receipts of canceled checks that substantiate deductions.  The IRS usually has up to three years after you file to audit you but may look back up to six years if it suspects you substantially underreported income or committed fraud.
Tax Returns with proof of filing and payment.

Keep Indefinitely

IRS forms that you filed when making non-deductible contributions to a traditional IRA or a Roth conversion.
Receipts for capital improvements that you've made to your home until seven years after you sell the house.
Retirement and Brokerage account statements unless you have access to them online.
Receipts for big-ticket purchases for as long as you own the item, to support warranty and insurance claims.

Toss

ATM Receipts once recorded
Bank deposit slips once the funds show up in your account
Credit card receipts after you get your statement unless you might return the item or need proof of purchase for a warranty
Credit card statements that do not have tax-related expenses on them