Numbers
Neartica lists 16 North American species.
Remarks
A very difficult genus, because most species are extremely similar in appearance and in morphology. In a given area, it is usually possible to learn the various species through experience, by learning which songs go with which crickets at what time of year. However, from photographs and even with pinned specimens it is very difficult if not impossible to identify many individuals with certainty. A few species are distinctive enough to recognize on sight, but most are not. This is a group where it is actually usually easier to identify a specimen by hearing it than by seeing it! Another complication is the fact that several species (especially in the west) do not even have names yet. And yet another complication is that females do not sing.
Knowing when and where a specimen is found is helpful (and in some areas there are only one or two species), but having a recording of the song as well is better.
Internet References
Singing Insects of North America has a pretty comprehensive key to Field (and other) crickets, plus sample songs of many species.