Why is the ionic product of water not divided by the concentration of water? I know the ionic product of water is $[\ce{H+}][\ce{OH-}]$, by following the equation:

$$\ce{H2O &lt;=&gt; H+ + OH-}$$

But actually it's just another way of writing:

$$\ce{2H2O &lt;=&gt; H3O+ + OH-}$$

Since, $K_\mathrm{w}=K_\mathrm{c}[\ce{H2O}]$ and

$$K_\mathrm{c}[\ce{H2O}]= \frac{[\ce{H3O+}][\ce{OH-}]}{[\ce{H2O}]}$$

Why can't the following equation be used? $$K_\mathrm{w}= \frac{[\ce{H3O+}][\ce{OH-}]}{[\ce{H2O}]}$$
The short answer is: substances in their standard form are not included in equilibria expressions, and most commonly this includes pure liquids and solids. 

The long answer is: the equilibrium expression relates all species to a standard activity (this is why they are all unitless). This question and answer detail that well.