You can use zref to measure the remaining space by saving the bottom position of the text and the one of the bottom of the frame. The following code works for me. It requires two runs after each change of text. It seems to work well
with different themes. If you want the image centered uncomment the \centering. I added a lower margin to not have it touch the bottom edge. You could also use a center environment which adds (rather large IMHO) margins by itself if you want.
Note that the environment restofframe can be used multiple times and all instances on one slide will share the remaining space equally.
\documentclass{beamer}
\usetheme{Berlin}
\usepackage{tikz}
\usepackage{zref-savepos}
\newcounter{restofframe}
\newsavebox{\restofframebox}
\newlength{\mylowermargin}
\setlength{\mylowermargin}{2pt}
\newenvironment{restofframe}{%
\par%\centering
\stepcounter{restofframe}%
\zsavepos{restofframe-\arabic{restofframe}-begin}%
\begin{lrbox}{\restofframebox}%
}{%
\end{lrbox}%
\setkeys{Gin}{keepaspectratio}%
\raisebox{\dimexpr-\height+\ht\strutbox\relax}[0pt][0pt]{%
\resizebox*{!}{\dimexpr\zposy{restofframe-\arabic{restofframe}-begin}sp-\zposy{restofframe-\arabic{restofframe}-end}sp-\mylowermargin\relax}%
{\usebox{\restofframebox}}%
}%
\vskip0pt plus 1filll\relax
\mbox{\zsavepos{restofframe-\arabic{restofframe}-end}}%
\par
}
\begin{document}
\begin{frame}
\frametitle{Title}
some texts
some texts
some text
some text
\begin{restofframe}
\begin{tikzpicture}
\draw (0,0) -- (1,1);
\draw (0,1) -- (1,0);
\end{tikzpicture}%
\end{restofframe}
\end{frame}
\begin{frame}
\frametitle{Title}
\framesubtitle{Subtitle}
some texts
some texts
some text
some text
\begin{restofframe}
\begin{tikzpicture}
\draw (0,0) -- (1,1);
\draw (0,1) -- (1,0);
\end{tikzpicture}%
\end{restofframe}
\end{frame}
\begin{frame}
\frametitle{Title}
\framesubtitle{Subtitle}
some texts
some texts
\begin{restofframe}
\begin{tikzpicture}
\draw (0,0) -- (1,1);
\draw (0,1) -- (1,0);
\end{tikzpicture}%
\end{restofframe}
some text
some text
\end{frame}
\end{document}

beamerframes have their content vertically centred. Consequently, you'll have to typeset something flush to the bottom in order to obtain the remaining height of the frame. Moreover,\pagegoaland\pagetotaldon't seem to be of help here in order to calculate the remaining "page" height. – Werner Sep 03 '11 at 05:52\pagegoaland\pagetotalbut I trust @Werner when he says they don't work withbeamer, which changes a lot of TeX internals. – Martin Scharrer Sep 09 '11 at 10:31