Ok to shred? The IRS has up to six years to audit people who neglect to report more than 25% of their income. So, if you are self-employed or have a complex tax situation, keep records at least that long. Some people I know keep their tax files for seven years, to be safe.
Also keep records showing the purchase date and price of stocks and mutual funds in taxable accounts until you sell the investments. Keep form 8606 (filed with your 1040), on which you report nondeductible contributions to a traditional IRA, until you withdraw all of the money.
Shred pay stubs if the information matches your W-2 for the year (unless you made charitable contributions via payroll deduction) and monthly brokerage statements when they match your year-end report. Most credit-card receipts, utility, and phone/cable bills can also go, unless you need them for tax purposes, such as to document home office or business expenses.