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\documentclass[a4paper]{article}

%% Language and font encodings
\usepackage[english]{babel}
\usepackage[utf8x]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{pgfplots} 
\pgfplotsset{compat=1.14}
\usepackage[a4paper,top=3cm,bottom=2cm,left=3cm,right=3cm,marginparwidth=1.75cm]{geometry}

\begin{document}
\begin{figure}[htb]
	\centering
	\begin{tikzpicture}
	\begin{axis}[
	width=0.9\textwidth,
	height=0.42\textheight,
	xlabel={},
        %symbolic x coords = {Fall 1, Fall 2},
	ylabel={Prozent}, 
	ymajorgrids,
	xmin=0, xmax=4,
	ymin=50, ymax=150, 
	ymajorgrids,
	xmajorgrids
	]	
	\addplot[green, only marks,mark=diamond*] coordinates {(0,80) (1,70) (1,60)};
	\addplot[red, only marks,mark=star] coordinates {(2,80) (3,70) (1,100)};
	\end{axis}
	\end{tikzpicture}
	\caption{Bruch}
\end{figure}
\end{document}

\documentclass{article}
\usepackage{pgfplots} 
\pgfplotsset{compat=1.14}% aktuell wäre 1.16

\begin{document} 
\begin{tikzpicture} 
  \begin{axis}[ 
    width=0.9\textwidth, 
    height=0.42\textheight, 
    xlabel={},
    ylabel={Prozent}, 
    ymajorgrids, 
    xmin=-0.5, xmax=5.5, 
    ymin=50, ymax=150, 
    minor x tick num=1,
    major x tick style={draw=none},
    minor x tick style={/pgfplots/minor tick length=1.5\baselineskip},
    xtick pos=lower,
    xtick align=outside,
    xminorgrids,
    extra x ticks={1,4},
    extra x tick labels={Fall 1, Fall 2},
    extra x tick style={ticklabel style={yshift=-2\baselineskip}},
  ]
  \addplot[green, only marks,mark=diamond*] coordinates {(0,80) (1,70) (1,60)}; 
  \addplot[red, only marks,mark=star] coordinates {(2,80) (3,70) (1,100)};
  \pgfplotsinvokeforeach{0,...,2}{\coordinate(c#1) at ({-.5+#1*3},0|-current axis.south);}
  \end{axis}
  \foreach \i in {0,...,2}\draw[help lines](c\i)--+(0,-4*\baselineskip);
\end{tikzpicture} 
\end{document}

extra x tick style={rotate=45,anchor=north east, text width=5cm,align=left},

\documentclass{article} 
\usepackage{pgfplots} 
\pgfplotsset{compat=1.14}% aktuell wäre 1.16 

\begin{document} 
\begin{tikzpicture} 
  \begin{axis}[ 
    width=0.9\textwidth, 
    height=0.42\textheight, 
    xlabel={}, 
    ylabel={Prozent}, 
    ymajorgrids, 
    xmin=-0.5, xmax=5.5, 
    ymin=50, ymax=150, 
    xtick={0,1,...,100},% <- eingefügt
    xticklabel={\pgfmathparse{int(mod(\tick,3)+1)}\romannumeral\pgfmathresult},% <- eingefügt
    minor x tick num=1, 
    major x tick style={draw=none}, 
    minor x tick style={/pgfplots/minor tick length=1.5\baselineskip}, 
    xtick pos=lower, 
    xtick align=outside, 
    xminorgrids, 
    extra x ticks={1,4}, 
    extra x tick labels={Fall 1, Fall 2}, 
    extra x tick style={ticklabel style={yshift=-2\baselineskip}},
  ] 
  \addplot[green, only marks,mark=diamond*] coordinates {(0,80) (1,70) (1,60)}; 
  \addplot[red, only marks,mark=star] coordinates {(2,80) (3,70) (1,100)}; 
  \pgfplotsinvokeforeach{0,...,2}{\coordinate(c#1) at ({-.5+#1*3},0|-current axis.south);} 
  \end{axis} 
  \foreach \i in {0,...,2}\draw[help lines](c\i)--+(0,-4*\baselineskip); 
\end{tikzpicture} 
\end{document}

extra x tick style={ticklabel style={anchor=north east,rotate=45, text width=5cm,align=left,draw}}