I have a Traditional IRA and a Roth IRA. This year my company introduced a Simple IRA.
As long the contributions to the Traditional+Roth are below the yearly limit, can I contribute to all three accounts?
Yes. You can make contributions to all three. However, you might not be able to deduct all of your contribution to the Traditional IRA and the Simple IRA.
Being able to take a tax deduction for a contribution to your Traditional IRA depends on
Employer sponsored plans include profit-sharing plans, 401(k) plans and Simple IRAs, which is what you mentioned. If the "Retirement Plan Box" on your Form W-2 is checked, then you are an active participant. If you are an active participant, you can take a tax deduction for a percentage amount, up to 100%, of your contribution, depending on your income and filing status.
You can definitely contribute to a Roth IRA too. However, according to the IRS for the 2011 tax year:
Contributions to a traditional IRA reduce your limit for contributions to a Roth IRA.
There is a chart in Publication 509 from the IRS that lets you figure how the Roth IRA contribution will affect your traditional IRA contribution limit.
This assumes you are making contributions to all three accounts, the Traditional, Simple and Roth IRA's in the same tax year.
I have found this document on the IRS website. Worksheet 1-2. Figuring Your Reduced IRA Deduction for 2011—Example 2 Illustrated on the document implies that both a regular IRA and SIMPLE IRA may be allowed. They calculate how much your IRA deduction is reduced by various other plans.
Enter your compensation minus any deductions on Form 1040 or Form 1040NR, line 27 (deductible part of self-employment tax) and line 28 (self-employed SEP, SIMPLE, and qualified plans). If you are filing a joint return and your compensation is less than your spouse's, include your spouse's compensation reduced by his or her traditional IRA and Roth IRA contributions for this year. If you file Form 1040 or Form 1040NR, do not reduce your compensation by any losses from self-employment
Still have not found a concise statement that allows both in the same tax year.
This article says you can. The Simple IRA may affect the ability to deduct the Traditional IRA from income, so the implication is that it's similar to a 401(k) in that regard. (I am still looking for IRS.gov articles to support this)