How can I prevent breaks in a custom environment?

\item is very complex. Replacing \item[] with \par\nobreak inserts a similarly-spaced (vertical) break yet allows control over the page breaking:

\newenvironment{Beispiel}[1][]
  {% \begin{Beispiel}[<title>]
  \goodbreak%
  \refstepcounter{examplecounter}%
  \begin{list}{}{\setlength{\rightmargin}{\leftmargin}}%
    \item[{\textbf{Beispiel~\theexamplecounter:}}]#1\par\nobreak}%
  {\end{list}}% \end{Beispiel}

One way would be to use the minipage environment.

\begin{minipage}{\textwidth}
\begin{Beispiel}[A title]
\begin{tabular}{ccc}
    1 & 2 & 3\\
    4 & 5 & 6\\
    7 & 8 & 9
  \end{tabular}
\end{Beispiel}
\end{minipage}