One option using amsthm and a new defined style (I also used \swapnumbers since your example suggests that you want numbers to appear before the name):
\documentclass{article}
\usepackage{amsthm}
\swapnumbers
\newtheoremstyle{newline}
{\topsep}%Space above
{\topsep}%Space below
{\itshape}%Body font
{}%Indent amount
{\bfseries}% Theorem head font
{}%Punctuation after theorem head
{\newline}%Space after theorem head
{}% Theorem head specification
\theoremstyle{newline}
\newtheorem{theo}{Theorem}
\begin{document}
\begin{theo}
A test theorem.
\end{theo}
\end{document}
The result:

The ntheorem package offers you the out of the box style changebreak:
\documentclass{article}
\usepackage{ntheorem}
\theoremstyle{changebreak}
\newtheorem{theo}{Theorem}
\begin{document}
\begin{theo}
A test theorem.
\end{theo}
\end{document}
The examples above will produce the head, a line break and then the body of the structure; if a complete blank line separating the head and the body is required, then you can modify my examples. For the first case, using amsthm, one could say something like
\documentclass{article}
\usepackage{amsthm}
\swapnumbers
\newtheoremstyle{newline}
{\topsep}%Space above
{\topsep}%Space below
{\itshape}%Body font
{}%Indent amount
{\bfseries}% Theorem head font
{\vspace{\baselineskip}}%Punctuation after theorem head
{\newline}%Space after theorem head
{}% Theorem head specification
\theoremstyle{newline}
\newtheorem{theo}{Theorem}
\begin{document}
\begin{theo}
A test theorem.
\end{theo}
\end{document}
which will now produce

but I find this extra spacing to be odd and wouldn't recommend this style. Something similar (defining a new style) can be done using ntheorem.
amsthm. – Gonzalo Medina Jan 13 '15 at 15:26