Yes, its possible to legally get a refund of more than the amount paid.
There are several tax credits that are refundable, which means that if the credit is more than the amount of your tax liability, the difference is refunded to you. As an example, the $8,000 first time home-buyer credit was refundable, so a person who owed $3000 in federal taxes could use the credit to pay their tax liability and get all of their tax payments back plus the extra $5000.
The most common refundable credits are the earned income credit (EIC) and the Additional Child Tax Credit (ACTC). Both of these are refundable credits for low income parents and its actually quite common that a parent with several children would get upwards of $5000 in extra refund (above what they paid in) from these credits.
Obviously there are strong feelings on both sides of these credits. I used to hate the EIC but I realized that its an incentive for people to work even though they might be just as well-off to collect welfare and food stamps. I'd rather see a single Mom work 40 hours a week, earn $20k and get an extra $6k from the federal government than see her sit at home and get $20k worth of food stamps, welfare, and government housing assistance.