You can safely dispose of single use batteries in household trash in all states except California, but you must take all other types to a recycling center. California law requires that residents take or mail all batteries to a recycling center.
Because manufacturers phased mercury out of certain single use batteries, they do not pose as much of an environmental threat as they did prior to 1996. It is still better for the environment to recycle all batteries and keep heavy metals out of landfills. In addition to recycling centers, cities frequently have recycling drop-off locations and recycling drop-off days at city halls.