If it is a polygon shapefile, then: SpatialPolygonsDataFrame
If it is a points shapefile, then: SpatialPointsDataFrame
If it is a lines shapefile, then: SpatialLinesDataFrame
They are defined in the sp package.
Importing shp files to those formats can be done many ways, but easily with shapefile function in raster package. This function, and others, usually go through gdal (see help for ?shapefile)