I have an existing shapefile that contains parcel data. I would like to add some of the existing parcels to a new shapefile. I am using ArcMap 10.1.
If you want a new shapefile, containing just some of the existing parcels, but no others, simply query for, or select the ones you want, then right-click on the layer select Data, then Export Data. If you have an existing shapefile follow the advise of @Maksim
Either make a selection of the polygons you need, right click, copy, then paste into your new shapefile in the interactive window.
Or, use append, to add the selected polygons to a shapefile of your choosing.