Same affiliation for all authors without extra packages

The simplest solution (which is not to say it is the best) is not to use \and.

\documentclass{article}
\title{Foo}
\author{Author One\qquad Author Two\\Affiliation}
\begin{document}
\maketitle
\end{document}

At the moment I see no other solution than using e. g. the authblk package. For details please refer to the package manual.

\documentclass[11pt,a4paper,english]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{babel}
\usepackage{authblk}
\usepackage{blindtext}

\title{Two Authors with same Affiliation}
\author{Author One}
\author{Author Two}
\affil{Affiliation}

\begin{document}
  \maketitle

  \blinddocument
\end{document}

The blindtext package is only for creating dummy text thus not part of the solution

For cleaner definition, another solution is to use the \publishers{} field of Koma-Script classes.

\documentclass{scrartcl}
\title{Foo}
\author{Author One \and Author Two}
\publishers{Affiliation}
\date{\today}                          %or \date{} to not print date
\begin{document}
    \maketitle
\end{document}

N.B.: use \and between each authors.