Start by looking at your income. There are income limits for Roth IRAs, so if your income is above those limits, then it's a no-brainer: a traditional IRA is the only one for you.
Let's say you're eligible for both a Roth and a traditional IRA. Generally, you're better off in a traditional if you expect to be in a lower tax bracket when you retire. By deducting your contributions now, you lower your current tax bill. When you retire and start withdrawing money, you'll be in a lower tax bracket, thereby giving less money overall to the tax man. If you expect to be in the same or higher tax bracket when you retire, you may instead want to consider contributing to a Roth IRA, which allows you to get your tax bill settled now rather than later.
But it can be difficult, if not impossible, to guess what tax bracket you will be in later in life, particularly if you've got a long way to go until you retire. So if you're not sure, another rule of thumb is to keep your retirement savings tax diversified, meaning you have accounts that will be both taxable and tax-free when you cash out in retirement. For example, if you already have a tax-deferred 401(k) plan through your employer, you might want to invest in a Roth IRA if you are eligible.
The Roth also offers more flexibility: You can withdraw your contributions (but not the earnings) without incurring a penalty so you have more access to your money. So if you've got a long way to go before retirement, and you're concerned about locking away your money for too long and want to be able to get at it if you need it, a Roth might be the way to go. 
