Button cells, also known as coin cells, are found in all sorts of equipment from watches to vacuum cleaners to computers and torches.  They have a wide range of sizes, voltages, and chemical composition.  They are based on either lithium, zinc, or silver chemistry.

From a human health perspective button cells are safe except with respect to children.  There are a number of cases of children ingesting batteries and consequently becoming ill. This would generally be for the higher energy lithium batteries when that are in a charged state.  Discharged zinc air batteries would pose a lower health threat.

Recycling
Button cells are able to be recycled to recover the materials.  To minimise environmental impact of the overall process it is best to stockpile them for as long as possible before having them recycled.  Button cells are relatively environmentally benign if disposed of into a sanitary landfills but recycling them has a  small environmental benefit.

Further information

• The Battery Controlled –  information on children and button cell safety
• Button cells at Wikipedia