Someone should make a "who killed the electric car... the FIRST time". As you rightly point out, electric cars were popular around the turn of the 20th century...
I believe that it's a 1909 Baker Electric.
To be fair, Jay's comment about not coming very far was referring to the range, and this has little to do with technology. Many of us can drive 90% of our commutes on the 35-40 miles that the Volt/Ampera will give on its battery. Clearly many of us can drive 100% of our commutes on the 70-80 miles that the LEAF will give on its battery. Admittedly, the GM drivers do their thing without massive range problems because of the "range extender" (ICE) and that LEAF drivers often rely heavily on en-route charging. Admittedly the Model S range of 200 miles is much more-comfortable for many drivers, but my point is that a 100-mile range is "about right". It doesn't really have much to do with technology - it has more to do with the demand for range.
There have been enormous developments in the technology, however: weight, size, capacity, management, speed, safety. I would expect more of that to come.
Back to the "who killed" thought, though, some quick web searches will tell you that Ford made some prototype electric cars. You'll also see that Ford and Edison were good friends. You'll find statements from each regarding the future of electric transport... both of them praising it at one time and denouncing it at others.
As I understand it these are the reasons why the electric car was killed the FIRST time:
1) electric cars cost more to produce than petrol cars and so there was more profit to be made selling petrol cars
2) Ford insisted on using Edison's batteries, and Edison's batteries were unreliable
3) Baker largely marketed their cars to women only
4) kerosene distribution was far more ubiquitous than electricity was at the time
5) Rockefeller (Standard Oil) sabatotauged electric car manufacture through its ties with Ford and Edison.
If this history of early technology development and the fighting between entrepreneurs and businessmen interests you, then I would recommend watching "The Men Who Built America"...
http://www.history.com/shows/men-who-built-america
http://en.wikipedia.org/wiki/The_Men_Who_Built_America
It doesn't touch on the electric car, but it shows the dynamics of collaboration and competition which will fuel logical support for the ideas above. Admittedly, the series focuses on America and mostly ignores that the rest of the world existed... which mindset is very American, indeed. Obviously any good historian would point out that most of these technologies and inventions originated outside of the United States and that these American entrepreneurs merely refined or expanded upon others' work.