"If I max out my 401k at work and my AGI is too high for a Roth or a deductible Traditional IRA, can I still make a non-deductible IRA contribution?"
The short answer to your question is YES you can. Anyone can make a non-deductible IRA contribution regardless of income as long as he/she or their spouse has earned income for the year they are making the contribution. More importantly why would you want to do so?
In the not so distant past, a lot of investors and advisors have strayed away from making or recommending non-deductible IRA contributions opting instead to invest this money in a taxable account. With the new tax laws in effect as of the beginning of this year (2013), non-deductible IRA contributions may be making a comeback especially with high income earners. Given that you earn above the Roth limits, your income may already exceed the $200,000 limit for an individual or $250,000 limit for a couple. Even if you aren’t over this limit, your investment earnings may put you over this limit. The reason I mention these limits is because a new tax law was implemented that taxes any investment earnings above this limit an additional 3.8% Medicare surtax. For people that earn above these limits, they will owe an additional 3.8% on their investment gains.
One way around this is a non-deductible IRA contribution as you mentioned. Though you can’t claim a deduction, at least you can defer the tax on all the earning within the account. This would avoid the additional Medicare surtax mentioned above and is an option worth considering. You may also be able to convert the contributions to a Roth IRA. The details of this conversion is somewhat complex and beyond the scope of your question.
I also want to emphasize that if you choose to make a non-deductible contribution, make sure you keep track of the amount that you contribute over the years and file this with the IRS using Form 8606. The last thing you want to do is be taxed again on the non-deductible contributions you made in the first place.
I hope this was helpful and that you read past the simple yes answer to your question. Please keep your questions coming as it is fun answering them.