They sure are. Handling, installing, and using CFL’s is perfectly safe and poses no health risk at all. If a bulb is broken, the powder inside contains a very small amount of mercury, so cleaning up the mess should be done carefully. The United States government has issued a set of instructions for this task should breakage happen.
Compact fluorescent bulbs come in a wide variety of colors, too. This means that you can use them even if traditional fluorescent lights give you headaches, for example. Try looking for CFL’s with a color temperature of 2,700K or 3,000K for the warmest, softest light color. If your headaches are from low light levels, compact fluorescent light bulbs can help you by allowing a brighter, whiter light in the same lamp that would only allow a lower light level standard bulb in the past.