Why is nitric acid such a strong oxidizing agent? In my teaching-lab experiments I've seen that nitric acid solutions are able to facilitate the dissolution of metals such as silver, even though they are more active than hydrogen. Does anyone know why nitric acid is so special? Why is it such a strong oxidizing agent?
Because, unlike in other metal dissolution reactions, the $\ce{H+}$ of $\ce{HNO3}$ isn't reduced&mdash;the $\ce{NO3-}$ is. The following data and balanced reactions are taken from Wikipedia:

\begin{align} 
  \ce{NO3- + 4 H+ + 3 e- &amp;-&gt; NO  + 2 H2O} &amp;
    E^\circ_\mathrm{red} &amp;= \pu{0.96 V} \\
  \ce{NO3- + 2 H+ +   e- &amp;-&gt; NO2 +   H2O} &amp;
    E^\circ_\mathrm{red} &amp;= \pu{0.79 V} \\
  \ce{Ag+(aq) + e-       &amp;-&gt; Ag(s)} &amp;
    E^\circ_\mathrm{red} &amp;= \pu{0.799 V}
\end{align}

Since the standard reduction potential (SRP) of the $\ce{NO2}$ reaction looks smaller than that of $\ce{Ag+}$ (I may be wrong, but by significant digits it can't be greater than $0.799$), one can conclude that it's the $\ce{NO}$ reaction that's occurring here. And the $\ce{NO}$ reaction has a large enough SRP to oxidise $\ce{Ag+}$.

Usually nitrogen compounds are pretty versatile when it comes to redox reactions, since nitrogen shows many oxidation states. So the simple reason for why $\ce{HNO3}$ is so strong an oxidising agent (with respect to other acids) is that it has a different, better path available to it to get reduced.

Note that the exact reduction path (i.e. final reduction products/oxidation state) depends upon the concentration of nitric acid&mdash;so much that copper can be oxidised in three different ways.