Why doesn't pure water conduct electricity?

Absolutely pure water is actually a poor electrical conductor, having a resistivity of 18.2 million ohms-cm. It is the amount of ionized substances (or salts) dissolved in the water which determines water's ability to conduct electricity. Materials such as copper and other metals which have valence electrons in their outer shells that are strongly repulsive of one another make good conductors because their electrons are easily moved through the metal. Atoms which have a stronger hold on their outermost electrons make good insulators and water, without ionizing impurities is an excellent insulator. But keep electrical appliances away from the bath tub because water is rarely pure.

P,

before I get down to answering your Q,
I think it is better if I state what electric current actually is.
Well,
all matter is made up of 'molecules' which contain "atoms" and "ions". These atoms and ions constitute of a much tinier particle named "electron".
the motion of a collective group of electrons induces a current

More aptly,
ELECTRIC CURRENT is a flow of electrons.

So, now coming to your Question:
As water is a covalent compound
wich has no free (i.e.mobile) ionz or electrons
it does not conduct electricity.

Hope I've helped.
Cheers,
Pin~Jinx / anarchist
[P.S.] frankvan, thnx for the tip!