Skipping line after "Proof" in proof environment

If this is to apply to all the proof environments in your document, you can redefine the proof environment to add \\* after the proof name has been written; here's such a redefinition (a \mbox{} will be necessary before \\*):

\documentclass{article}
\usepackage{amsthm}
\usepackage{lipsum}% just to generate text for the example

\makeatletter
\renewenvironment{proof}[1][\proofname]{\par
  \pushQED{\qed}%
  \normalfont \topsep6\p@\@plus6\p@\relax
  \trivlist
  \item[\hskip\labelsep
        \itshape
    #1\@addpunct{.}]\mbox{}\\*
}{%
  \popQED\endtrivlist\@endpefalse
}
\makeatother

\begin{document}

\begin{proof}
\lipsum*[1]
\end{proof}

\end{document}

Use \hfill:

\begin{lemma}
balbla
\begin{proof}
\hfill
\begin{enumerate}
\item one
\item two
\end{enumerate}
\end{proof}
\end{lemma}

Instead of redefining the proof environment, you could define your own, based on proof but leaving the old proof intact, and you need just one line:

\newenvironment{myproof}[1][\proofname]{\proof[#1]\mbox{}\\*}{\endproof}

Using a new name makes also clear, that it's a different proof environment. Further, you are still able to use the original proof in cases when you don't like a line break, for example if the proof would consist of one short equation or a reference.

Complete example:

\documentclass{article}
\usepackage[english]{babel}
\usepackage{blindtext}
\usepackage{amsthm}
\newenvironment{myproof}[1][\proofname]{\proof[#1]\mbox{}\\*}{\endproof}
\begin{document}
\begin{myproof}
\blindtext
\end{myproof}
\begin{myproof}[Proof sketch]
\blindtext
\end{myproof}
\end{document}