Label Points in a circle in tikz

As a typical counterpart to tikz drawings, here's a take on the pstricks version.

\documentclass{article}
\usepackage{pst-node}% http://ctan.org/pkg/pst-node
\usepackage{multido}% http://ctan.org/pkg/multido
\begin{document}

\begin{pspicture}(10,10)
  \SpecialCoor
  \psset{unit=3cm,runit=3cm}% Scaling of x,y and r units
  \pnode(3,0){O}% Circle origin
  \pscircle(O){1}% Outer circle
  \degrees[20]% 20 angles per 360 degrees (each angle is 18 degrees)
  \rput(O){\multido{\i=1+1}{20}{% Cycle through 20 angles and relocate relative to circle origin
    \pcline(O)(1;\i)% Print line from origin to circle edge
    \uput{5pt}[\i]{\i}(1;\i){\i}% Print label with rotation
  }}
\end{pspicture}
\end{document}

Modifying the label command to

\uput{5pt}[\i]{0}(1;\i){\i}% Print label without rotation

yields

Printing labels at for every odd index is possible by using

\ifodd\i\uput{5pt}[\i]{\i}(1;\i){\i}\fi% Print ODD label with rotation

while

\ifodd\i\else\uput{5pt}[\i]{\i}(1;\i){\i}\fi% Print EVEN label with rotation

prints only even indices. Here's an illustration of the latter (print EVEN labels with rotation) choice:

This can be combined with no rotation of every node as well. For this modify the appropriate parameter in the \uput command, which is defined by

\uput{<labelsep>}[<refangle>]{<rotation>}(<coordinate>){<stuff>}

This rotates <stuff> by angle <rotation> at distance <labelsep> and angle <refangle> from <coordinate>. In my example, using \degrees[<n>] divides 360 degrees into <n> angles. So, it allows you to use these angles (as numbers, where angle=i*(360/<n>)). Also, because of \SpecialCoor, one can use polar coordinates - represented by (<r>;<t>) - or Cartesian coordinates - represented by (<x>,<y>). pst-node allows for substituting any of these <coordinate> types with a node <name> defined by (say) \psnode(<coordinate>){<name>}, as was done in the MWE.

A friend of mine once needed kind of a cake to visualize fractions. Adding rotated nodes wasn't hard:

\documentclass{scrartcl}
\usepackage{tikz}
\usetikzlibrary{intersections, calc, fpu, decorations.pathreplacing}

\newcommand{\TikZFractionalCake}[5]{% Num, Denom, Color, Borders, Size
    \pgfmathsetmacro{\angle}{360/#2};%
    \foreach \x in {1,...,#1}%
    {   \pgfmathsetmacro{\lox}{\x-1}%
        \filldraw[draw=#4,fill=#3] (0,0) -- (\angle*\lox:#5) arc (\angle*\lox:\angle*\x:#5) -- cycle;%
        \pgfmathsetmacro{\mix}{\x-0.5}%
        \node[rotate=\mix*\angle] at (\mix*\angle:#5+0.3) {\x};
    }
}   

\begin{document}

\begin{tikzpicture}
\TikZFractionalCake{20}{20}{white}{black}{3}
\end{tikzpicture}

\end{document}

---

Sure, makes it even easier:

\documentclass{scrartcl}
\usepackage{tikz}
\usetikzlibrary{intersections, calc, fpu, decorations.pathreplacing}

\newcommand{\TikZFractionalCake}[5]{% Num, Denom, Color, Borders, Size
    \pgfmathsetmacro{\angle}{360/#2};%
    \foreach \x in {1,...,#1}%
    {   \pgfmathsetmacro{\lox}{\x-1}%
        \filldraw[draw=#4,fill=#3] (0,0) -- (\angle*\lox:#5) arc (\angle*\lox:\angle*\x:#5) -- cycle;%
        \node[rotate=\x*\angle] at (\x*\angle:#5+0.3) {\x};
    }
}   

\begin{document}

\begin{tikzpicture}
\TikZFractionalCake{20}{20}{white}{black}{3}
\end{tikzpicture}

\end{document}

---

That is possible indeed:

\documentclass{scrartcl}
\usepackage{tikz}
\usetikzlibrary{intersections, calc, fpu, decorations.pathreplacing}

\newcommand{\TikZFractionalCake}[6]{% Num, Denom, Color, Borders, Size, k-th label
    \pgfmathsetmacro{\angle}{360/#2};%
    \foreach \x in {1,...,#1}%
    {   \pgfmathsetmacro{\lox}{\x-1}%
        \filldraw[draw=#4,fill=#3] (0,0) -- (\angle*\lox:#5) arc (\angle*\lox:\angle*\x:#5) -- cycle;%
    }
    \pgfmathsetmacro{\secondstep}{2*#6}
    \pgfkeys{/pgf/number format/.cd,int detect,precision=2}
    \foreach \x in {#6,\secondstep,...,#1}%
    {   \node[rotate=\x*\angle] at (\x*\angle:#5+0.3) {\pgfmathprintnumber{\x}};
    }
}   

\begin{document}

\begin{tikzpicture}
\TikZFractionalCake{21}{21}{white}{black}{3}{3} 
\end{tikzpicture}

\end{document}

You have several solutions :

1) you can mix tkz-euclide with tikz

\documentclass{minimal}
\usepackage{tkz-euclide}
\begin{document}

\begin{tikzpicture}[scale=1]
\tkzDefPoint(0,0){O}
\tkzDrawCircle[R](O,3 cm)
\def\sectors{20}
\foreach \i in {1,2,...,\sectors} {
    \tkzDefPoint({\i*360/\sectors}:3){P\i}    
    \tkzDrawSegment[color=black](O,P\i)
      \node[label=18*\i:\i] at  (P\i) {} ;
}
\end{tikzpicture}
\end{document}  

\end{document} 

3) you use only tikz ! (see Tom' solution)

4) I forgot this one ( I have some difficulties to work with my personal packages). I put like you scale=3 but when it's possible I avoid the use of scale.

\documentclass{minimal}
\usepackage{tkz-euclide}
\begin{document}

\begin{tikzpicture}[scale=3]
\tkzDefPoint(0,0){O}
\tkzDrawCircle[R](O,1 cm)
\def\sectors{20} 
\tikzset{label style/.style={} }; 
\foreach \i in {1,2,...,\sectors} {
    \tkzDefPoint({\i*360/\sectors}:1){P\i} 
    \tkzDrawSegment[color=black](O,P\i)
      \tkzLabelPoint[label=360/\sectors*\i:\i](P\i){}
}
\end{tikzpicture}
\end{document}

5) It's possible to place the label on the radius but I think it's not a good typographic idea

\documentclass{minimal}
\usepackage{tkz-euclide}
\begin{document}

\begin{tikzpicture}[scale=3]
\tkzDefPoint(0,0){O}
\tkzDrawCircle[R](O,1 cm)
\def\sectors{20} 
\tikzset{label style/.style={} }; 
\foreach \i in {1,2,...,\sectors} {
    \tkzDefPoint({\i*360/\sectors}:1){P\i} 
    \tkzDrawSegment[color=black](O,P\i)
} 
% it's possible to avoid the next loop with conditional macro ...
\foreach \i in {1,3,...,\sectors} {% you can change what you want here
            \tkzLabelPoint[rotate=18*\i,right](P\i){\i} ;
}  
\end{tikzpicture}
\end{document}