The IRS can come back and check your tax returns for the last 3 years. But it is a good idea to keep your financial information longer than that. You may have questions come up in a legal matter 10 years from now that the tax return and financial records could help.
The IRS recommends individual tax returns be kept at least seven years. If you have storage I'd keep them up to 10. Obviously, companies should probably keep them forever!
IRS goes back 3 years to check tax returns. Most people say that keeping your tax returns for 5 years is sufficient. I, myself, believe that in order to be on the safe side keeping your returns for 7 years is safer yet.