Another way to see a lot of variable relationships and a lot of correlations in a compact space is Kevin Wright's corrgram.
# this is the second reproducible section - the vote dataset is part of corrgram
library("corrgram")
corrgram(vote, order=TRUE, upper.panel=panel.cor, main="vote")
It's good, but also a little cumbersome and corrgram can be really slow. There's also nothing wrong with just firing plot() from the console to see things one by one, but what about a sort of dataset browser application? Like maybe written in Shiny?