While far from the norm, there have been some instances where CFL light bulbs have begun to smoke or smolder because the product is defective or improperly installed. In cases like these, it's important to know the basics.
As Energy Star states on its official website, qualified CFL light bulbs feature self-extinguishing capabilities, which means that they should never catch fire. Additionally, while CFL bulbs contain mercury, as long as the glass tube remains intact, no mercury is released from the bulb.
Any odor caused by a smoking or smoldering bulb is likely to be unpleasant, but it is not harmful.
If a CFL light bulb begins to smoke or smolder, it is recommended that you immediately turn off its power source. Once it has cooled, you should then remove it from the light socket and dispose of it.
It is also suggested that you drop off CFL light bulbs at an ALA-member lighting showroom so they can be recycled. In fact, this could be a law in your specific area depending on where you live.
If disposal is allowed at your home, place any fluorescent bulbs in a plastic bag and seal them before putting them in the garbage. Never incinerate a CFL or any other mercury-containing product.