There are several basic individual retirement savings options: Traditional IRA, Roth IRA, 401(k) and Annuities. For now, let focus on Traditional IRA. You can contribute to a traditional IRA whether or not you are covered by another retirement plan. However, you may not be able to deduct all of your contributions if you or your spouse is covered by an employer-sponsored retirement plan. Thus, Traditional IRA contributions can be either deductible or nondeductible. If your tax situation does not make you eligible for contribution into deductible IRA, the IRS rules will not preclude you from contributing into nondeductible IRA. However, it raises a question whether this is a smart move. Probably not and here is why.
You do not get the tax benefit (i.e., tax deduction) in the current year from your contribution. When it comes time for you to withdraw money from your nondeductible IRA, it is almost guaranteed that you will get into some type of "argument" with the IRS on what part of your contributions is tax not taxable. It would help your argument if you were able to prove your position with copies of Nondeductible IRAs Form 8606, but for that you had to be diligent enough to file this form and maintain appropriate copies. Here the IRS can be quite helpful, because filing of this form is a requirement. If the IRS found out that you did not file Form 8606, they would send you a friendly reminder along with a $50 penalty for failing to file.
Even if you do everything right, when you start withdrawing money, you're still in for a bit of a surprise. You will not be able to withdraw money completely tax-free from a Nondeductible IRA. You will have to withdraw your non-taxable contribution proportionately with the taxable income. To illustrate, consider this example: if you contributed over the years a total of $6,000 to your Nondeductible IRA and your account is now worth $15,000. Since your contributions represent 40% of the total value, only 40% of any withdrawals you make will be free of tax.
With all the hassles outlined above, you are probably better off with a Roth IRA. You still do not get the deduction from income in the year of contributions, but there are no forms to file and your withdrawals are tax-free. (at least for now).