There is a very simple way in ArcGIS to create a new layer from a selected set of features in a feature class or shapefile (for those who haven't yet switched to a geodatabase).
 |
| Source: rla.unc.edu |
This created layer can remain virtual if you do not want to keep the data for later reference, or it can be exported as a shapefile or feature class if you want to preserve it. See the step-by-step guide below on how to use Create Layer from Selected Features.