There are some income limits and contribution limits on who can contribute to an IRA.
Generally speaking, as long as you or your spouse is earning taxable income, you can contribute money to an IRA, be it a Roth or a Traditional IRA.
There are limits at which you cannot contribute to a Roth IRA (in 2016, the limit is $132,000 for a single filer and $194,000 for a married couple). There are also income limits at which you are no longer able to deduct contributions to a Traditional IRA, but these are only applicable if you or your spouse has a qualified retirement plan at work.
There are no income limits which can lock you out of a traditional IRA otherwise. It is actually possible to leave contributions in a traditional IRA when you aren’t able to deduct the contributions, and this is known as a non-deductible IRA.
This account will grow tax-deferred, but the fact that it holds after-tax contributions and most of it will be taxed as ordinary income upon withdrawal, it is not utilized very often. The income limits are all adjusted for inflation, so you should check with the IRS website and your accountant to make sure you have the correct information for your situation.
With these limits, there is also usually phase-out up to limit, which will limit your contributions or ability to deduct them.