The London Underground 1908 - The "Tube Map"
Above: 1932 - Harry Beck's redesign. It is initially rejected by the commission, but after 300,000 copies are distributed due to high demand the argument ends.
The New York City Subway System
1948 - NYC Subway Map:
Massimo Vignelli's 1972 redesign:
Unlike Beck's London Underground system (which Vignelli had been influenced by) the above streamlined design was never truly accepted. In 1979 the map reverted back to its more literal design and all of the anterior content was again included. Below is a detail of the 1979 map design:
Vignelli has since designed the map again in 2008 and launched a digital version in 2012. Read an article here about Vignelli's reaction to the map's numerous reiterations and a short explanation behind his more sophisticated design.
Other designs have been attempted as well. The Kick Map (below, center) came out in 2007 as a hybrid of Vignelli's version (right) and the more recent (left) designs:
And I couldn't leave out Veit Schuetz's illustration for the 2000 Cosmic Art Enterprise annual art exhibition: