How long you need to keep tax records will depend on jurisdiction. In general, if you discard records in a period of time less than your tax authority recommends, it may create audit problems down the road. ie: if you make a deduction supported by business expense receipts, and you discard those receipts next year, then you won't be able to defend the deduction if your tax authority audits you in 3 years.
Generally, how long you keep records would depend on: (a) how much time your tax authority has to audit you; and (b) how long after you file your return you are allowed to make your own amendments.
In your case (US-based), the IRS has straight-forward documentation about how long it expects you to keep records:
Period of Limitations that apply to income tax returns
Keep records for 3 years if situations (4), (5), and (6) below do not apply to you.
Keep records for 3 years from the date you filed your original return or 2 years from the date you paid the tax, whichever is later, if you file a claim for credit or refund after you file your return.
Keep records for 7 years if you file a claim for a loss from worthless securities or bad debt deduction.
Keep records for 6 years if you do not report income that you should report, and it is more than 25% of the gross income shown on your return.
Keep records indefinitely if you do not file a return.
Keep records indefinitely if you file a fraudulent return.
Keep employment tax records for at least 4 years after the date that the tax becomes due or is paid, whichever is later.
Note that the above are the minimum periods to keep records; for your own purposes you may want to keep them for longer periods than that. For example, you may be in a position to discover that you would like to refile a prior tax return, because you forgot to claim a tax credit that was available to you. If you would have been eligible to refile in that period but no longer have documentation, you are out of luck.