Try some definitions:
\makeatletter
\let\LTX@item\@item
\def\my@item[#1]{\LTX@item[#1]\hfill}
\def\rebinditem{\let\@item\my@item}
\def\revertitem{\let\@item\LTX@item}
\makeatother
Then use them as follows:
\begin{frame}
\frametitle<presentation>{Euclid's algorithm}
\begin{minipage}{.65\textwidth}
\begin{enumerate} \rebinditem % <<<-----
\item Pseudo-code:
\item {\tt function GCD($a$, $b$) \{}
\begin{itemize}%\revertitem %<<-- uncomment if desired
\item {\tt if ($b =0$) return $a$;}%
\item \raggedleft {\tt Let $r$ be the remainder\\ when you divide $a$ by $b$}% <<--- multiline item needs \raggedleft
\item {\tt return GCD($b$, $r$);}%
\end{itemize}
\item \}
\end{enumerate}
\end{minipage}
\end{frame}
This approach should work with any document class, not just beamer.

\raggedleft
(aka "right-aligned")itemize
list supposed to look like? Should each item's "bullet" be\raggedleft
as well, or should the bullets be left-aligned whereas the contents should be right-aligned? Please advise.