Typeset a series of characters with equal distances?

Make sure you typeset them it math-mode, i.e. $-$ and $+$.

Be aware that it makes a difference if you use a single math-mode or separate ones for them. The last sign has different spacing in the first case because it is taken as an unary sign but the others are operators.

Compare the following:

documentclass{article}

begin{document}

$-$$-$$-$$+$$+$$+$

$+$$+$$+$$+$$+$$+$

$-$$-$$-$$-$$-$$-$

$---+++$

$++++++$

$------$

end{document}

Result:

---

For the alignment with the other signs a, A and 0 I would recommend that you make macros for all and set the width manually the one of the widest (should be $+$).

This can be done either with hbox to <length>{hss <sign>hss} (TeX) or using makebox[<length>][c]{<sign>} (LaTeX). The width is provided by settowidth{<length register>}{<content>}.

documentclass[11pt, a4paper]{scrreprt}

usepackage{booktabs}

newlength{slength}
settowidth{slength}{$+$}
newcommand*{Sz}{makebox[slength][c]{0}}
newcommand*{SA}{makebox[slength][c]{A}}
newcommand*{Sa}{makebox[slength][c]{a}}
newcommand*{Sp}{makebox[slength][c]{$+$}}
newcommand*{Sm}{makebox[slength][c]{$-$}}

begin{document}

begin{tabular}{cc}
toprule
         1 &  SpSpSm  
         2 &  SpSmSp  
         3 &  SmSpSp  
         4 &  SzSzSz  
         5 &  SmSmSm  
         6 &  SzSzSz  
midrule
         7 &  SmSpSm  
         8 &  SzSzSz  
         9 &  SpSmSm  
        10 &  SmSmSp  
        11 &  SpSpSp  
        12 &  SzSzSz  
midrule
        13 &  SzSzSz  
        14 &  SzSzSa  
        15 &  SzSzSA  
        16 &  SzSASz  
        17 &  SASzSz  
        18 &  SzSaSz  
        19 &  SaSzSz  
        20 &  SzSzSz  
bottomrule
end{tabular}

end{document}

Result:

An easy way to achieve this would be to typeset the plusses and minuses in a monospace font with verb|+-+-|

There are however issues with verbatim text which you might run into... Another solution might be to use texttt and macros for your plusses etc. Here's an example:

documentclass{article}
usepackage[T1]{fontenc}
newcommandp{+}
newcommandm{-{}}
begin{document}
texttt{++---++}

texttt{ppmmmpp}

texttt{++mm aA0}
end{document}

You need to use a macro like this for the minus sign because otherwise they get turned into en-dashes if you use the fontenc package. This should also mono-space letters easily.

one possible form to typeset your table would be to use a table column for each character:

documentclass[11pt, a4paper]{scrreprt}
usepackage{booktabs}

newcommandPl{${}+{}$}
newcommandMi{${}-{}$}

begin{document}

begin{tabular}{cc@{hspace{-2pt}}c@{hspace{-2pt}}c}
  toprule
  1 & Pl & Pl & Mi 
  4 & 0 & 0 & 0 
 12 & a & 0 & A 
 15 & 0 & 0 & A 
  bottomrule
end{tabular}

end{document}

Michel's solution is nice, but I'd like to present some improvements.

newlength{stretchlen}
settowidth{stretchlen}{+}
newcommand{stretchit}[1]{realstretch#1_}
newcommandrealstretch[1]{%
  ifx#1_%
  else
    makebox[stretchlen]{ifx#1-$-$else#1fi}%
    %hbox to stretchlen{hssifx#1-$-$else#1fihss}%
    expandafterrealstretch
  fi}

It's not necessary to have splitterm and to define temp at each stage, since we're collecting tokens one by one and those tokens are simple characters. It's best also to set stretchlen to the widest character, in this case +. Finally, there's the particular case of - that should be treated differently with a $-$.

I've left commented the line with hbox: with makebox it's more in the LaTeX way of thinking; the two lines give the same result, but of course makebox is a bit less efficient than hbox.

---

Some years later, the solution can be made more robust, with the possibility of managing other characters that need special treatment.

documentclass[10pt,a4paper]{scrreprt}

usepackage{booktabs}
usepackage{collcell}
usepackage{array}
usepackage{xparse}

ExplSyntaxOn
NewDocumentCommand{stretchit}{m}
 {
  tl_map_inline:nn { #1 }
   {
    makebox[stretchlen]
     {
      str_case:nnF { ##1 }
       {
        {-}{$-$}
        {+}{$+$}
        {*}{$*$}
       }
       {##1}
     }
   }
 }
ExplSyntaxOff

newlength{stretchlen}
AtBeginDocument{settowidth{stretchlen}{$-$}}

begin{document}

begin{tabular}{r >{collectcellstretchit}c<{endcollectcell}}
midrule
 1 & ++- 
 2 & +-+ 
 3 & -++ 
 4 & 000 
 5 & --- 
 6 & 000 
midrule
 7 & -+- 
 8 & -*x 
 9 & +-- 
10 & --+ 
11 & +++ 
12 & 000  
bottomrule
end{tabular}  

end{document}

A quick and dirty solution might be to enclose the symbols in braces: ${-}{+}{+}{+}$ looks better than $-+++$, as LaTeX won't try to interpret each + or - as a binary operator.