It is possible to make non-deductible contributions to an IRA, even if you have a qualified plan at work. Traditional IRAs are a good place to stash retirement money because of the tax treatment.
Some people will choose to make contributions even when they are not deductible, which gives us two kinds of Traditional IRAs: deductible and non-deductible.
Deductible IRAs provide a way to lower your taxes because you can deduct contributions to your IRA from your income. Nondeductible IRAs do not allow you to deduct your contributions, but they still retain their tax-deferred growth. Unlike a Roth, these after-tax contributions will be taxed upon withdrawal as income.
Non-deductible IRAs are only utilized in circumstances where the individual is in a high tax bracket and is unable to find a better tax-advantaged place to invest some of his or her money. An individual in this situation would probably already be participating in and maximizing contributions to a qualified plan at work, and would be unable to contribute to a Roth due to income limitations.
Non-deductible IRAs will have a cost basis that does not get taxed upon withdrawal in retirement, but it will be reduced based on a formula that takes other qualified contributions into account, which may cause some of the funds in the account to be double-taxed (on contribution and distribution).
In general, it is probably not recommended to use a non-deductible IRA, since other after-tax investment options exist which will enjoy the milder capital gains taxes, even if they do not grow tax-deferred.