Animation in Enumerate list - Beamer

Whie Herbert has given you one option, here are few more.

\uncover

\documentclass{beamer}
\begin{document}
\begin{frame}
\begin{enumerate}
\uncover<1->{\item Hi}
\uncover<2->{\item Hello}
\uncover<3->{\item Hi again}
\uncover<4->{\item Hello again}
\end{enumerate}
\end{frame}
\end{document}

\only

\documentclass{beamer}
\begin{document}
\begin{frame}
\begin{enumerate}
\only<1->{\item Hi}
\only<2->{\item Hello}
\only<3>{\item Hi again}   %% note absence of - after 3
\only<4->{\item Hello again}
\end{enumerate}
\end{frame}
\end{document}

To avoid jumping, you may use overlayarea:

\documentclass{beamer}
\begin{document}
\begin{frame}
\begin{overlayarea}{\textwidth}{.5\textheight}
\begin{enumerate}
\only<1->{\item Hi}
\only<2->{\item Hello}
\only<3>{\item Hi again}   %% note absence of - after 3
\only<4->{\item Hello again}
\end{enumerate}
\end{overlayarea}
\end{frame}
\end{document}

\pause

\documentclass{beamer}
\begin{document}
\begin{frame}
\begin{enumerate}
\item Hi \pause
\item Hello \pause
\item Hi again \pause
\item Hello again 
\end{enumerate}
\end{frame}
\end{document}

If you want only one item per slide

\documentclass{beamer}
\begin{document}
\begin{frame}
\begin{enumerate}
\item<1> Hi 
\item<2> Hello 
\item<3> Hi again 
\item<4> Hello again
\end{enumerate}
\end{frame}
\end{document}

Can be done automatically:

\documentclass{beamer}
\begin{document}
\begin{frame}
\begin{enumerate}[<+->]
\item Hi
\item Hello
\end{enumerate}
\end{frame}
\end{document}

For all lists write into the preamble:

 \beamerdefaultoverlayspecification{<+->}