Can one make an annual non-deductible, non-Roth IRA contribution even if your income levels are above the threshold that would prevent a deductible IRA?

[SusanY1]

Yes, you can make nondeductible contributions to a Traditional IRA even if your income levels are above the threshold for a deductible contribution.  Only taxpayers who do not have sufficient taxable compensation from work are excluded from being able to make these contributions. 

[Opus 17]

Yes.  This creates a non-deductible basis in your IRA that is reported on form 8606.  When you withdraw in retirement, a portion of your withdrawal is tax-free.   For example, suppose you contributed $50,000 that was deductible, $20,000 that was non-deductible, and you have tax-free growth so the total value is $100,000.  In this example, 20% of any withdrawal would be tax-free, because it is a withdrawal of your non-deductible basis.  Your new non-deductible basis is also tracked on form 8606 and used to calculate the non-taxed amount of future withdrawals.

For this reason, you should keep copies of any form 8606 that is part of your tax return for as long as you live.  If you lose the forms and can't prove your non-deductible basis, the IRS can tax the entire withdrawal even though you already paid tax on part of the money.  Form 8606 is an exception to the usual rule that you can discard tax papers after 3-6 years.