Your error bars may be giving you a hint to look more closely at the distribution of your data: it may not be symmetric. For example, if your data is essentially log-normal you could work with the logs of your numbers and the problem will automatically go away.

I'm not a fan of error bars. In theory they let you visually do some statistical significance estimates and perhaps give some sense of the underlying data. But there are a lot of subtleties and at least one study has found that even experienced scientists often misinterpret them. This [nice blog post][1] discusses some of the issues.

If you do need to summarize the data with a few statistics, I'd argue for [boxplots][2] as a better way to represent asymmetric distributions, along with text/captions that highlight important statistical significance conclusions.


  [1]: http://scienceblogs.com/cognitivedaily/2008/07/31/most_researchers_dont_understa_1.php
  [2]: http://en.wikipedia.org/wiki/Box_plot