There is a statistical test for exactly this kind of problem--it is called Pearson's Chi-Squared test. It is able to determine if an observed distribution of results, such as the results of rolling a die, matches a theoretical distribution, such as one where every number occurs equally as often.
The test requires at least 5 expected occurrences for each event (each number, in our die case). This means you would need at least 6*5=30 rolls of the die.
You can conduct the tests in excel, as it conveniently has chi squared test formula you can use. You just plug in your observed frequencies and your theoretical frequencies, and it tells you how often a fair die rolls as "bad" as what you rolled. If a fair die would roll that bad less than 5% of the time, you probably should be suspicious about your die.
Remember that these statistical test are not perfect. A fair die can still roll poorly, or a weighted die can roll like a fair one, purely by random chance. No test can protect against these random occurrences. You also have to adjust your cutoff value when testing multiple dice. Just imagine that if you tested 100 fair dice, some are likely to roll very poorly. You would easily expect to see results that a fair die would produce only 1% of the time. A good rule of thumb for adjusting your cut-off is to divide 5% by the number of dice you are testing.
I created a spreadsheet you can view online to test your own dice. You just roll your dice and record your results, and your spreadsheet tells you the odds that a fair dice would roll worse than you just did. It also tells you a cut-off value to use to determine if your dice are fair. Check it out at http://1drv.ms/1pLgjzO
You can see more about the statistical test on Wikipedia at http://en.wikipedia.org/wiki/Pearson%27s_chi-squared_test