It depends on what kind of IRA it is. Almost anyone can contribute to a traditional IRA, provided you (or your spouse) receive taxable income and you are under age 70 ½. But your contributions are tax deductible only if you meet certain qualifications. For more on those qualifications see Who can contribute to a traditional IRA?
Roth IRA contributions are never tax deductible, and you must meet certain income requirements in order to make contributions. For 2012, your modified adjusted gross income must be $183,000 or less if you are married and filing jointly; $125,000 or less if you are single, head of household or married filing separately (and didn't live with your spouse at any point during the year). Those who make slightly above these limits may still be able to make partial contributions. For more see Who can contribute to a Roth IRA?
SIMPLE and SEP IRAs are for self-employed individuals or small business owners. To set up a SIMPLE IRA an employer must have 100 or fewer employees earning more than $5,000 each. And the employer cannot have any other retirement plan besides the SIMPLE IRA. Any business owner or individual with freelance income can open a SEP IRA.