The husband participates in his employer's 401K, while the wife is unemployed. Assuming this couple does not exceed the AGI or MAGI limits for a Traditional IRA, will each of them be able to contribute to a Traditional IRA?
Provided that you had earned income in 2013, you can always open a Traditional IRA for 2013 (or make a contribution for Year 2013 to an existing Traditional IRA) as long as you were under age 70.5 on December 31, 2013. If you did not have earned income in 2013, you can nonetheless make a contribution to your Traditional IRA as long as your spouse had earned income, you are under age 70.5, and you file a joint return with your spouse. What is restricted is the ability to deduct the amount of the contribution from current income, and that ability is determined not only by whether you are covered by a retirement plan at work (even if you have chosen to not participate in the plan) and your income level (which you are already aware of) but also your tax filing status.
From Publication 590 (edition dated 1/6/2014) from the IRS
For 2013, if you are covered by a retirement plan at work, your IRA deduction will not be reduced (phased out) unless your modified AGI is:
More than $59,000 but less than $69,000 for a single individual (or head of household),
More than $95,000 but less than $115,000 for a married couple filing a joint return (or a qualifying widow(er)),
- Less than $10,000 for a married individual filing a separate return.
(Note: these numbers are scheduled to increase slightly for 2014 contributions).
If you do not meet these requirements, some or all of your Traditional IRA contribution will not be deductible from your current income. The nondeductible part of the contribution can stay in your IRA if you like, and if you leave it in there, it becomes part of the basis (the sum of the post-tax contributions) of the IRA . The basis amount is not taxed when you withdraw it since you have already paid tax on it but any earnings from the basis that have accumulated within the IRA are taxable when withdrawn. You need to file Form 8606 with your income tax return to report any changes in basis to the IRS.
So, suppose that you are not age 70.5 as yet, and you are earning mucho big bucks so that none of your Traditional IRA contribution for Year 2013 is deductible. Your spouse has no earned income but nonetheless made a contribution to the spouse's IRA and you are filing a joint return for Year 2013. @JoeTaxpayer clarifies OP Geo's question asking
"Is the spouse's IRA contribution deductible even if yours isn't?"
The answer is, "It depends on what mucho big bucks means" Publication 590 says
If you either live with your spouse or file a joint return, and your spouse is covered by a retirement plan at work, but you are not, your deduction is phased out if your modified AGI is more than $178,000 but less than $188,000. If your modified AGI is $188,000 or more, you cannot take a deduction for contributions to a Traditional IRA.
(Note: these numbers are also scheduled to increase for 2014).
Thus, it would appear that if the modified AGI on your joint return is more than $115K but less than $178K, then you cannot deduct your IRA contribution but your nonworking spouse (or even a working spouse who is not covered by a retirement plan at work) can deduct the IRA contribution. Hmmmm, weird twist in the rules that I never knew existed.