How to export a dataset with "SpatialPolygonsDataFrame" as a shapefile

Wesley's answer is correct. So to specifically export the tornado data you need to do:

library(GISTools)
library(rgdal)
data(tornados)

writeOGR(obj=torn, dsn="tempdir", layer="torn", driver="ESRI Shapefile") # this is in geographical projection

writeOGR(obj=torn2, dsn="tempdir", layer="torn2", driver="ESRI Shapefile") # this is in equal area projection

For R both of these datasets are simply treated as SpatialPointsDataFrames.

> class(torn)
[1] "SpatialPointsDataFrame"
attr(,"package")
[1] "sp"

> class(torn2)
[1] "SpatialPointsDataFrame"
attr(,"package")
[1] "sp"

Note there is also a function in the maptools package to accomplish this, namely writeSpatialShape:

library(maptools)
writeSpatialShape(torn, "torn").

See ?writeSpatialShape for options.

You should look at the rgdal package, specifically the writeOGR function.

For example, I first downloaded the 110m-resolution "States and Provinces" shapefiles from Natural Earth, unpacking them to ~/scratch/ne_110m_admin_1_states_provinces. I read them into R via:

library(rgdal)
setwd("~/scratch")
states <- readOGR(dsn="ne_110m_admin_1_states_provinces",
    layer="ne_110m_admin_1_states_provinces")

At this point, the object states is a SpatialPolygonsDataFrame. Now I create a new directory ("tempdir") and save the shapefiles there:

dir.create("tempdir")
writeOGR(obj=states, dsn="tempdir", layer="states", driver="ESRI Shapefile")

The shapes are now saved to the directory ~/scratch/tempdir, as files states.shp, etc. You can do the same thing with a SpatialPointsDataFrame, just see the first example in the documentation of the writeOGR function.