The amount you should save depends on your overall financial plan, but you should aim to put as much in an IRA as the government allows you to. That's because the more you save in a tax-favored account, the more tax-protected gains you can rack up.
If you're younger than 50, your 2016 contributions to a traditional IRA or a Roth IRA are limited to $5,500 or the total of your taxable compensation, whichever is smaller. If you're 50 or over before the end of the year, you're allowed to contribute up to an additional $1,000 for a total yearly contribution of $6,500; this is the IRS's way of encouraging you to save more in the final years before retirement.
However, the amount you can contribute to a Roth IRA also depends on your income. To make the full contribution in 2016, your modified adjusted gross income must be less than $117,000 if you're single, or $184,000 as a married couple filing jointly. If you earn slightly above those amounts, you may be able to make smaller contributions.