One solution, which seems to work quite well, is to compare your map to a geographical dictionary such as Merriam-Webster's Geographical Dictionary. Search for place names that are listed on the map in the geographical dictionary to find out when they existed based on the historical information in the dictionary. By searching for multiple places, you can often narrow down the date of the map to a range of a few years.
On a world map, Africa is a great place to search for places that narrow the date of your map. For example, if a map of the world shows Rhodesia as a country, it was probably printed between 1970 and 1980. By utilizing other places on the map, you can pinpoint its approximate creation date.
Online, the Replogle: How Old is Your Globe? site provides an excellent list of country names that you can use to date a map or globe.
In addition, the Getty Thesaurus of Geographic Names provides historic information about places around the world. Happy dating!