Volatile organic compounds (VOCs) are carbon-containing compounds that tend to evaporate readily. There doesn't seem to be a universally-accepted technical definition. Some sources define VOCs as organic compounds that boil at less than 200 degrees Fahrenheit; other definitions reference a vapor pressure of greater than 0.1 millimeters of mercury under standard conditions.
The US EPA's Terms of Environment defines a VOC as "Any organic compound that participates in atmospheric photochemical reactions except those designated by EPA as having negligible photochemical reactivity." If that's not confusing enough check out the defintion in the U.S. Code of Federal Regulations at 40 CFR Part 51.100(s) (Link is via the Iowa Department of Natural Resources). Wikipedia adds to the fun by throwing in some international definitions.
However defined, there are many different VOCs. Environmental regulations focus on a relatively small fraction of those, generally VOCs that see wide industrial use, are breakdown products of industrial chemicals, and/or are compounds known to be particularly toxic.
There are many laboratory methods for analyzing VOCs. One of the most widespread is EPA's SW-846 Method 8260. There are several variants of this method, but they all include most of the compounds that attract the lion's share of interest at hazardous waste sites. Here is a list of the compounds included in Method 8260B:
2-Chloroethyl vinyl ether