If you want to clear the center of the footer, then you have to use \cfoot{}, clearing the center footer.
If the center pagenumber on the title page should vanish, too, then use \thispagestyle{empty} after \maketitle
\documentclass[a4paper]{article} %sætter dansk standard, a4 papir.
\usepackage{fancyhdr}
\pagestyle{fancy}
\lhead{Some name}
\rhead{Some title}
\usepackage{lastpage}
\usepackage{etoolbox}%
\rfoot{\thepage\ af \pageref{LastPage} }
\cfoot{}%
% Remove the `plain` - pagestyle and replace it by `fancy`
\patchcmd{\maketitle}{\thispagestyle{plain}}{\pagestyle{fancy}}{}{}%
\begin{document}
\title{A title}
\date{Some date}
\author{some name}
\maketitle
\thispagestyle{empty}%
\newpage
hello world
\end{document}

Improved version
\documentclass[a4paper]{article} %sætter dansk standard, a4 papir.
\usepackage{fancyhdr}
\usepackage{lastpage}
\usepackage{etoolbox}%
\fancypagestyle{titlepage}{%
\fancyhf{}% Clear all the fields first
\renewcommand{\headrulewidth}{0pt}%
\renewcommand{\footrulewidth}{0pt}%
\rfoot{\thepage\ af \pageref{LastPage}}%
}%
\patchcmd{\maketitle}{\thispagestyle{plain}}{
\pagestyle{titlepage}%
\clearpage%
}{}{}
\begin{document}
\title{A title}
\date{Some date}
\author{some name}
\maketitle
\newpage
\pagestyle{fancy}%
\lhead{Some name}
\rhead{Some title}
\rfoot{\thepage\ af \pageref{LastPage} }
\cfoot{}%
hello world
\end{document}
\cfoot{\thepage\ af \pageref{LastPage}}or\cfoot{} \rfoot{\thepage\ of \pageref{LastPage}}? – moewe Sep 08 '14 at 10:31