PSTricks: Wrong axis labels

You've got conflicting directives going on for the x-axis. Try something like:

\documentclass{article}

\usepackage{pstricks-add}

\def\sandsynlighed#1#2{%
  \psframe[
    linecolor=red,
    fillstyle=solid,
    fillcolor=blue!50
  ](#1,0)(!#1 \bredde add #2 4 div)
}

\psset{unit=0.75}

\begin{document}

\def\bredde{1.5 }
\begin{pspicture}(-0.9,-0.5)(14.3,11.3)
  \psaxes[
    xlabelOffset=-0.75,
    %%Ox=-1,
    %%dx=1.5,
    xLabels={0,1,2,3,4,5,6_{+0},6_{+1},7},
    Dy=2,
    dy=0.5
  ]{->}(14,10)[$X$,0][$100 \cdot P(X)$,90]
  % Sandsynlighederne.
 \sandsynlighed{0}{18.70}
\end{pspicture}

\end{document}  

UPDATE

Given your comment, here's a fairly different approach. Here I delved into the pst-plot package to look at how labels are placed and copied some of the code. The key here is the \multido macro. Also, since the label positions are enumerated with \nA, but we're stepping by 2, I added another counter \nB to extract the correct label from \psk@xLabels. All this is wrapped up in the macro \myxlabels

To get the desired spacing, I set the xunit to a new value. Perhaps you may not want to do this globally. If so, then just reassign xunit within a group enclosing the pspicture.

Also, you don't need to add the extra space to \bredde as you did. You can use \space in the call to the post-script commands.

Here's a new MWE:

\documentclass{article}

\usepackage{pstricks-add}

\def\sandsynlighed#1#2{%
  \psframe[
    linecolor=red,
    fillstyle=solid,
    fillcolor=blue!50
  ](#1,0)(!#1 \bredde\space add #2 4 div)
}

\makeatletter
\def\myxlabels#1{\def\psk@xLabels{#1}%%'
      \multido{\nA=1+2,\nB=0+1}{10}{\uput{\psxlabelsep}[-90]{\pst@xLabelsRot}(\nA,0)%%'
      {\strut\pshlabel{\psPutXLabel{\nB}}}}%%'
}
\makeatother

\psset{unit=0.75,xunit=0.75}

\begin{document}

\def\bredde{2}
\begin{pspicture}[](-0.9,-0.5)(14.3,11.3)
  \psaxes[
    dx=2,
    xLabels={,},
    Dy=2,
    dy=0.5
  ]{->}(20,10)[$X$,0][$100 \cdot P(X)$,90]
  %% Sandsynlighederne.
  \myxlabels{0,1,2,3,4,5,6_{+0},6_{+1},7}

 \sandsynlighed{0}{18.70}
\end{pspicture}

\end{document}  

the offset was not working for special label setting. Try pst-plot.tex from http://texnik.dante.de/tex/generic/pst-plot/ Then use something like:

\documentclass{article}
\usepackage{pstricks-add}    
\def\sandsynlighed#1#2{%
  \psframe[linecolor=red,fillstyle=solid,
           fillcolor=blue!50](#1,0)(!#1 \bredde add #2 4 div)}

\psset{unit=0.75}
\begin{document}

\def\bredde{1.5 }
\begin{pspicture}(-0.9,-0.5)(14.3,11.3)
  % Akserne.
  \psaxes[
    xunit=1.5,
    xLabels={,0,1,2,3,4,5,6_{+0},6_{+1},7},
    xlabelOffset=-0.75,
    Dy=4,dy=1,
  ]{->}(9,10.75)[$X$,0][$100 \cdot P(X)$,90]
  % Sandsynlighederne.
  \sandsynlighed{0}{18.70}
\end{pspicture}

\end{document}