Conductivity of electrically ionized water So we see people putting salt in water for increased conductivity.
What if you ionize the water with voltage. Positive and negative splitting. One side will have more free electrons than the other right? Will that side then be a better conductor?
 A: In perfectly pure (demineralized) water there are no excess electrons or other particles. There are only water molecules. Nothing to accumulate on one side.
Since water molecules are dipoles, by adding a voltage across it you can align those molecules so their positive and negative ends, respectively, are pointing in the same direction. The positive end of each molecule is attracted to the side of lower potential; the negative end towards the side of higher potential. In total, the attraction to either side cancels out - such dipole only aligns (rotate), it doesn't move (translate).
(A high enough current can cause dielectric breakdown, like when lightning is suddenly conducted through otherwise insulating air - that requires a voltage large enough to actually break apart the molecules. I believe that is not your intention.)
Adding salt to water to make it conducting is simply done because salt dissolved into ions.  These ions have a net-charge and are positive and negative. They are not dipoles, so they will move (translate) at an applied voltage. And here you have your current carriers in the form of moving charges.
Bottom line: Perfectly pure water is not conductive at all. (Water in equilibrium does get a little bit partially ionized from smaller chemical reactions that break a few molecular bonds - see Floris' comment) 
