EVs offer some definite advantages, and lots of advantages that depend on the specifics.
They definitely reduce local pollution - unlike fossil cars, they don't emit NOx, CO2, CO or particulates. And they are much easier to decarbonise than fossil cars - they just need renewable electricity to recharge.
So in general, yes, electic cars are a significant improvement over their fossil-fuel guzzling competitors. (And it's rather bizarre to hope that the batteries end up at a landfill after just 3 years of life. But if that were the case, no, that would not be remotely sustainable.)
In terms of their advantages over petrol (gasoline) & diesel, it will depend on just how your electricity is generated, and what the full lifecycle costs are of each vehicle.
Presently, at least here in the UK, a lot of electric-car suppliers are leasing, rather than selling, the batteries, which means that they'll go back to the manufacturer at the end of their life for complete recycling. After all, a dead battery contains all the ingredients needed to make a brand-new battery - the thing that needs doing, is reversing all the decay chemistry, which is just a question of energy inputs.
As I wrote over on skeptics.SE:
Electric cars are about 4x as efficient as fossil-fuelled combustion engines, tank-to-wheel: ICE engine efficiency is around 20%. Electric engines tend to be around 80-90%. For the whole-cycle energy-efficiency, then well-to-wheel would be the efficiency you were after, and then it would be very sensitive to how your electricity would be generated.
For the nitty-gritty of the energy consumption of electric, fossil and hydrogen cars, see this paper from George Wallis of the Claverton Energy Group (pdf, 317kb).
Note that pretty much all electric cars benefit from regenerative braking, and very few fossil-cars do.
Efficiencies do depend on the drive cycle: and whereas ICEs tend to be optimised for speeds around 85km/h, the efficiency of electric cars decreases with increasing speed, just as the core physics would lead you to expect:
For more information on efficiencies power-station to wheel of electric vehicles, see the US Gov Fuel Economy site.