If I give someone a map and they talk about the map more than the data, I have failed.
~Kristin Warry, GISgroup, LinkedIn
Assuming your map audience isn’t cartographers*, this statement is a perfect way to describe how effective map design should be in most cases: extremely usable. It takes very good design skills and a lot of time to make a map that is so useable that people forget about the mode of communication and listen only to the message.
Some of the best examples of informative and non-showy mapping come from the New York Times. Here are a few:
Hurricane Irene Damage Map
Joe Burgess, Amanda Cox, Alicia Parlapiano, Archie Tse, Lisa Waananen, Tim Wallace
Mapping America, Census Map
Matthew Bloch, Shan Carter, Alan McLean
Super Bowl 2011 Twitter Chatter Map
Matthew Bloch and Shan Carter
* If you show a map to cartographers, of course they’ll talk about the map design. A few other exceptions exist as well, such as when a map is made primarily for advertising purposes, in which case it may be more beneficial to make something outlandish that attracts attention first, and is useable, second. Another exception is brand-new map design inventions, which may take a while for people to become accustomed to before they pay attention the actual data (e.g., subway map style, the recent facebook friendship map.)