Jake's answer is good, but if you really want to obey the minimum height, i.e. allow the nodes also to be larger you would need to measure the height (actually the depth) by yourself and increase it if required. You can code an own environment for this which takes the width and totalheight as two arguments.
The height argument can also be replaced by reading out the minimum height argument using \pgfmathsetlength\pgf@yb{\pgfkeysvalueof{/pgf/minimum height}}%.
\documentclass{report}
\usepackage{tikz}
\usetikzlibrary{positioning}
\makeatletter
\newenvironment{minsizebox}[2]{%
\pgfmathsetlength\@tempdima{#2}%
\pgfmathsetlength\pgf@yc{\pgfkeysvalueof{/pgf/inner ysep}}%
\advance\@tempdima by -2\pgf@yc
\begin{lrbox}{\@tempboxa}%
\begin{minipage}[t]{#1}%
\vspace{0pt}%
}{%
\end{minipage}%
\end{lrbox}%
\ifdim\@tempdima>\dp\@tempboxa
\dp\@tempboxa=\@tempdima
\fi
\box\@tempboxa
}
\makeatother
\begin{document}
\tikzset{every node/.style={rounded corners,minimum height=5cm}}
\begin{tikzpicture}
\node[draw,fill=yellow] (n1) {%
\begin{minsizebox}{5cm}{5cm}
alignment of nodes
with \verb|minipage|
long text
fourth line
\end{minsizebox}%
};
\end{tikzpicture}
\begin{tikzpicture}
\node[draw,fill=yellow] (n1) {%
\begin{minsizebox}{5cm}{5cm}
alignment of nodes
with \verb|minipage|
long text
long text
long text
long text
long text
long text
long text
\end{minsizebox}%
};
\end{tikzpicture}
\begin{tikzpicture}
\node[draw,fill=yellow] (n1) {%
\begin{minsizebox}{5cm}{5cm}
alignment of nodes
with \verb|minipage|
long text
long text
long text
long text
long text
long text
long text
long text
long text
long text
long text
long text
long text
long text
long text
long text
\end{minsizebox}%
};
\end{tikzpicture}
\end{document}

\node [text width=<dimension>]then TikZ adds theminipagefor you. – Martin Scharrer Jul 07 '11 at 08:47pgfmoduleshapes.code.tex) where theminimum heighthandling is implemented forrectanglenodes. The vertical centering of text boxes in the node is hard coded there, so there aren't any TikZ style to adjust this. Maybe this is worth a feature request!? – Martin Scharrer Jul 07 '11 at 09:00