You have one too many ands in your question and there are a couple of caveats. You can max out your 401(k) and a Roth OR a Traditional IRA. Let me explain...
Your 401(k) and IRA are essentially disconnected. So you can max out your 401(k) and contribute $5,500 to IRAs (plus $1,000 if you are over 50). But there are limitations.
The bottom line is: Accounting for the three conditions above, the maximum amount you can contribute to all your IRAs (Roth/Traditional or a combination thereof) is $5,500 (plus catch-up if appropriate) and this amount is not affected by the amount you contribute to a 401(k)
There are combined limits for qualified and non-qualified plans and certain compensation limits. You can contribute more to your IRA in 2013. For both traditional IRAs and Roths, the maximum you can contribute is now $5,500 (the catch-up contribution is still $1,000 for people age 50 or older, bringing their total to $6,500 in 2013). The maximum you can contribute to a 401(k) is $17,500 in 2013. The catch-up contribution limit for people age 50 or older remains at $5,500. Helpful information can be found on the IRS website http://www.irs.gov/uac/2013-Pension-Plan-Limitations
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You can contribute to a traditional or Roth IRA whether or not you participate in another retirement plan through your employer or business. However, you might not be able to deduct all of your traditional IRA contributions if you or your spouse participates in another retirement plan at work. Roth IRA contributions might be limited if your income exceeds a certain level.
Curt did a great job answering your question. Assuming you fully max out your tax-deferred retirement vehicles, your next step would to be to look at the fees you are paying in all your accounts and the tax efficiency of your taxable savings. Generally speaking you can grow your retirement assets more effectively the less fees you are paying, so look to invest in broad based, low cost index funds if possible. Make sure when you look at your overall portfolio that most of your bond holdings are in your tax deferred accounts and that your taxable accounts contain tax efficient, low cost equity index funds or ETFs.
While the answers above are great, the one thing you should consider is whether or not your IRA contribution will be deductible or not for 2013 based on the income guidelines.
If you participate in a company sponsored retirement plan, your IRA contribution may not be deductible.
For single filers who are covered by a company retirement plan in 2013 the deduction is phased out between $59,000 and $69,000 of adjusted gross income.
For married filers if you are covered by a company retirement plan in 2013 the deduction is phased out between $95,000 and $115,000 of adjusted gross income.
For married filers where you are covered by a company plan but your spouse is not, in 2013 the deduction for your spouse is phased out between $178,000 and $188,000 of adjusted gross income.
Curt gave you great parameters. here are some pratfalls to avoid.
Keep in mind that there are income limits on what is tax deductible into a traditional IRA and income limits on when you can even contribute to a Roth IRA. If you reach your income limits on tax-deductibility on a traditional IRA, you can contribute after-tax; then later convert it to a Roth. I don't recommend you co-mingle after tax monies with pre-tax monies in the same IRA.
Also, be sure that your 401(k) has what is called 'safe harbor'. If not, you may run into something called a 'corrective distribution'.
I would suggest that if you either do not have safe harbor on your 401(k) or you have situations where you may have pre-tax dollars and after-tax dollars in a retirement plan, that you seek guidance from a qualified financial planner in your area, preferably a CFP(R). Regardless, you might want to seek professional guidance.