How to get only one vertically centered equation number in align environment with two equations

Use aligned instead.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation}
\begin{aligned}
  dr_t &= \kappa ( \theta - r_t ) dt + \sigma_r r^{\xi} dW_t \\
  dA_t &= \mu A_t dt + \sigma_A^{\alpha} dZ_t, 
\end{aligned}
\end{equation}
\end{document}

Here's a slightly better way to do this (IMO):

Using the split environment within an align will produce one equation number, vertically centered within the split (so long as there's not a page break involved, as discussed here).

Note that you can have individual labels for each equation by adding \label{} to the end of each line before the line break \\

For example:

\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}

\begin{document} 

\begin{align}
  E_1&=A+B \label{eq:1}\\
   \begin{split}
    E_2&=(C-D)E_1 \label{eq:2}\\
    &\quad +[(1-R)+R(1-Y)\\
    &\quad +\pi(1-\delta)]E_2\\
    &\quad +F\cdot E_3
   \end{split}\\
  E_3 &=(\pi\cdot \chi)-(R\cdot E_1)-(RY\delta\cdot E_2) \label{eq:3}
\end{align}

\end{document}

which gives:

This is really a comment on TH.'s accepted answer (which should stay that way). Using just one aligned doesn't work if you have multiple columns: they are separated by only a small space, since aligned "shrinks to fit". The workaround is to use one aligned per column, and wrap the whole thing in a larger align, like so:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
 \begin{align}
  \begin{aligned}
   x &= y \\       f(x) &= f(y)
  \end{aligned}
  &&
  \begin{aligned}
   a &= b \\       g(a) &= g(b)
  \end{aligned}
 \end{align}
\end{document}

This should produce two pairs of equations, each aligned at the equals sign, and with one equation number centered between the lines.