Spacing in beamer seems to change when \pause is added

Yes, \pause inserts "something" on an empty line in your instance. You could get rid of it by "jumping back" a line using \vspace*{-\baselineskip} before \pause:

\documentclass{beamer}% http://ctan.org/pkg/beamer
\begin{document}
\begin{frame}
  Without pause:
  \[A\]\[B\]
  Not too much space between displayed equations.
\end{frame}
\begin{frame}
  With pause:
  \[A\]\vspace*{-\baselineskip}\pause\[B\]
  Too much space between the equations.
\end{frame}
\end{document}​

Usually it's not recommended to use one displayed equations right after the other. In such cases you would do something like

\begin{gather*}
A \\ B
\end{gather*}

The problem is that \pause doesn't work reliably in amsmath environments, but you can use the fix from this answer of mine:

\documentclass{beamer}
\makeatletter
\let\save@measuring@true\measuring@true
\def\measuring@true{%
  \save@measuring@true
  \def\beamer@sortzero##1{\beamer@ifnextcharospec{\beamer@sortzeroread{##1}}{}}%
  \def\beamer@sortzeroread##1<##2>{}%
  \def\beamer@finalnospec{}%
  }
\makeatother
\begin{document}
\begin{frame}
  Without pause:
  \begin{gather*}
    A \\
    B
  \end{gather*}
  Not too much space between displayed equations.
\end{frame}
\begin{frame}
  With pause:
  \begin{gather*}
    A \\ \pause
    B
  \end{gather*}
  Same space between the equations.
\end{frame}
\end{document}

Let me point out that the spacing differs from the one you get with \[A\]\[B\]. On the one hand, gather doesn't "see" that the line Without pause is short, so it puts more vertical space between that line and A. On the other hand, the space between A and B becomes smaller; this can be adjusted by using \\[1ex] instead of \\. (Adjust the 1ex to your needs.)

---

If you want to stick with two seperate displays: as Werner said, \pause inserts something (namely, one or two \pdfliterals) on an otherwise empty line, which gives an additional vertical space of one \baselineskip. One can prevent TeX from ever putting this additional vertical space by using

\par\pause\noindent

instead of \pause: the \par ends the empty line after the first display, the \noindent keeps the empty line before the second display empty (and \parskip is zero in beamer); see also this answer of mine for details.