Send in the coolest (or most useful, if you want to be practical about it) plot you can find. If you send it to me (rosem@uoregon.edu), I can add it to this post, or you can just include it in a comment.

So far, Paul is winning (see p. 81-83, and check out the R code on p. 123):
Correlating Maps (Yeah, that’s right – you can correlate maps.)

A much simpler plot, but still really lovely (check out the gorgeous semi-transparent overlapping!):
linear profiles with error envelopes (code)

And plotting networks!
visualizing networks

Bump plots, great for showing rank changes over time (includes some R Shiny!)
Bumps charts

Animated plots, both in 2D and 3D. Pretty bad ass.
http://alstatr.blogspot.com/2014/02/r-animating-2d-and-3d-plots.html

Plotting ggplot in plotly (great way to make website-friendly plots!)
http://ropensci.org/blog/2014/04/17/plotly/

Arc plots (in this case, showing network connections between Star Wars characters)
post
step-by-step description of how to make arc plots
R code

Some awesome plots via Matt:
I do really like the map visuals people have created, though, with packages like ggmap. Here is a map of Twitter activity in Europe done in R.
twitter map

I also like the animations some people do for iterative or time series data (which can be done with the catools package or in combination with the Imagemagick app). Here’s a cool Bayesian monte carlo simulation being visualized:
animated MC simulations!

and, more perilously, a plot of pirate attacks from 1978 to present (both of these use Imagemagick, which you call from R using the system() command):
Pirates in Rrrrrr! (I couldn’t resist)