The pH of a neutralized solution
TL;DR
The neutral point is not the same as the equivalence point.
A neutral aqueous solution at room temperature, $25~^\circ\mathrm{C}$ and standard pressure $1~\mathrm{atm}$, has always $\ce{pH}=7$.



If you look for credible sources of definitions of neutral solutions on the internet, most likely you will find something along the lines of this:  


  Neutral solution
  (Science) Has a $\ce{pH}$ level of $7$: a solution in which the concentration of hydrogen ions and hydroxide ions are equal (biology-online.org)


Or even worse:


  Neutral Solution Definition:
  An aqueous solution with a $\ce{pH}$ of $7.0$ $(\ce{[H^{+}]} = 1.0 \times 10^{-7}~\mathrm{M})$. (chemistry.about.com)


The second one especially is negligent of a lot of features.
Unfortunately the IUPAC does not provide an actual definition of a neutral solution. There are two possible definitions, which come to the same conclusion (compare the above), given the same external conditions.


The lazy definition:
The concentrations of hydronium and hydroxide ions are identical. $$c(\ce{OH-})= c(\ce{H3O+})$$
In terms of $\ce{pH}, \ce{pOH}, \mathrm{p}K_w$ one arrives at a more complete side.
Pure water is a neutral solution. It's autoprotolysis provides 
\begin{align}
\ce{2H2O &amp;~&lt;=&gt;~ OH- + H3O+}.\tag{1}\\
\end{align}
Now we can formulate the equilibrium constant and furthermore assume that autoprotolysis is small compared to the overall concentration of water.
\begin{align}
  K_c &amp;= \frac{c(\ce{OH-})\cdot c(\ce{H3O+})}{c^2(\ce{H2O})}\\
  K_w &amp;= c(\ce{OH-})\cdot c(\ce{H3O+})\tag{2}\\
\end{align}
Equation $(1)$ also provides the lazy definition. $$c(\ce{OH-})= c(\ce{H3O+})\tag3$$
We plug that into $(2)$ and we arrive at
$$c(\ce{H3O+})=\sqrt{K_w}\tag{4}$$
Consider the actual definition of 
$$\ce{pH} = −\lg a(\ce{H+}) = −\lg\left( m(\ce{H+}) \gamma_m(\ce{H+}) / m^\circ\right)\tag{5}$$ rewritten using concentrations
$$\ce{pH} = −\lg a(\ce{H+}) = −\lg\left( c(\ce{H+}) \gamma_c(\ce{H+}) / c^\circ\right)\tag{5a}$$ 
The identities used here are $a(\ce{H+})$ for the activity of a proton in aqueous solution, $\ce{H+ (aq)}$ and we will consider $\ce{H+ (aq) = H3O+}$ to be the same. Now we are going to assume, that the activity coefficient is $\gamma_c(\ce{H+})\approx 1$ for very diluted systems. Using the standard concentration $c^\circ$ we do not have to care about units.
$$\ce{pH} = −\lg\left( \frac{c(\ce{H+})}{c^\circ}\right)\tag{5b}$$
Now we can substitute in $(4)$ and we will have a nice definition of the $\ce{pH}$ of a neutral solution.
$$\ce{pH} = −\lg\left( \frac{\sqrt{K_w}}{c^\circ}\right)\tag{6}$$


The second formulation includes a very crucial point. The autoprotolysis $(1)$ is temperature, $T$, dependent, which is obvious following the definition of the standard equilibrium constant
$$ K^\circ = \exp\left\{\frac{-\Delta G^\circ}{\mathcal{R}T}\right\}\approx K_c.$$
Therefore also the ion product of water is temperature dependent, $K_w(T)$. 
Wikipedia actually has a couple of values for the $\mathrm{p}K_w$. Reaction $(1)$ is endothermic. A higher temperature means providing energy, means a higher $\mathrm{p}K_w$. For example, in the human body, $37~^\circ\mathrm{C}$, this value is slightly higher than for the one we usually assume as the "neutral point" $\mathrm{p}K_w(25~^\circ\mathrm{C})=14$.

Since $(6)$ is more correct in the following form,
$$\ce{pH}(T) = −\lg\left( \frac{\sqrt{K_w(T)}}{c^\circ}\right)\tag{6a},$$
the neutral $\ce{pH}(T)$ therefore changes with temperature.

Another note is that it is also pressure dependent, but that might take it a little too far.

The equivalence point is usually defined for an arbitrary chemical reaction between an acid and a base, and it refers to the situation where there are stoichiometric quantities of acid and base are present.
$$\ce{AH + B &lt;=&gt;[\ce{H2O}] A^- + HB+}$$
This means, that at the equivalence point the following statement holds:
$$c_\text{initial}(\ce{HA}) = c_\text{final}(\ce{HB+}).$$
Therefore the $\ce{pH}$ at the equivalence point will only be governed by the reactions of $\ce{HB+}$ and might not be neutral.



The issue of solvent dependency is addressed by Fred Senese quite concise on antoine.frostburg.edu:


  pH is often used to compare solution acidities. For example, a solution of pH 1 is said to be 10 times as acidic as a solution of pH 2, because the hydrogen ion concentration at pH 1 is ten times the hydrogen ion concentration at pH 2. This is correct as long as the solutions being compared both use the same solvent. You can't use pH to compare the acidities in different solvents because the neutral pH is different for each solvent. For example, the concentration of hydrogen ions in pure ethanol is about 1.58 × 10-10 M, so ethanol is neutral at pH 9.8. A solution with a pH of 8 would be considered acidic in ethanol, but basic in water!