Air travel, while statistically safer than nearly every other form of transportation, doesn't come without its share of risks. Unfortunately, those risks go up with airlines based in poorer countries, where safety regulations may not be as strict as in the U.S. Sunday's New York Times addresses the safety issue and details three useful websites for researching which carriers have good safety records and which are best avoided.
Probably the best resource is the International Air Transport Association (IATA), which provides a list of its member airlines, each of which has undergone "an extensive safety audit."
Unlike the IATA, which is an industry group invested in helping its airlines maintain good safety records, the European Union is seeking to protect its citizens, and therefore has a blacklist of carriers it won't allow to serve EU airports.
Since the Federal Aviation Administration (FAA) is willing to accept the IATA's audits, it doesn't extensively check each airline. However, the FAA does look at whether foreign governments have the means to effectively watch over the airlines based in their countries, and has a list (in a downloadable Excel file) of nations that meet the standards of the International Convention on Civil Aviation, and those that don't.
Part of the planning process for any trip to a developing country should include at least a visit to each of the above sites. If it looks like you might need to fly on a suspect airline, think about alternatives. Train travel is a great way to see the sights and perhaps reduce the risks as well.