This truly is a frequently asked question! And like so many things, the answer is “It depends”.
At a bare minimum, you should keep tax records for at least 3 years after the due date of your tax return, or two years after you paid the tax (if later). Therefore, you should keep your 2014 tax records at least until April 15, 2018, if you filed and paid by the due date. Tax records for this purpose is proof of items of income and deduction found on your tax return. For an individual or couple without a business, these would be things like W-2s, 1099 forms for interest and investment income, and proof of the deductions you took if itemizing deductions, such as bank statements and canceled checks, property tax statements, and acknowledgments of charitable contributions. For a business, this would also include your business books and records, and receipts for business expenses.
As a practical matter, most people choose to keep these records for seven years.
For business or rental property, you should keep records of acquisition of business assets (land, buildings, equipment) for at least 3 years after you’ve disposed of them. For traded assets, keep the original records at least 3 years after you’ve disposed of the traded item.
There are lots more rules and situations not covered above. IRS has a pretty good list at this link.