My home does NOT have forced-air heating, and, therefore, there is no duct work. Can I still get central air conditioning?

Absolutely! Today simple, ductless air conditioning options make it possible to install a quiet, efficient air conditioning system in your home even if it doesn't have ductwork. 
Ductless air conditioning systems consist of one or more indoor air-distribution units linked by refrigeration lines to an outdoor compressor. These flexible “hoses” can be positioned inside your walls and ceilings with a minimum of inconvenience. Installing ductless air conditioning costs a little more than standard central air conditioning systems but much less than the cost of installing ductwork and a central air-conditioner.