\documentclass{standalone}
\usepackage{pgfplots}
\usepackage{pgfplotstable}
\pgfplotsset{compat=1.10}
\pgfplotstableread{
0.01 1.00
0.02 2.00
0.03 3.00
0.04 4.00
0.05 5.00
}\datatable
\begin{document}
\begin{tikzpicture}
\begin{axis}[ymin=0, ymax=6]
\addplot table {\datatable}
node[pos=0.0, pin=above:"Unidentified peak"]{} % pos only allows for fractional value
node[pos=0.2, pin=above:"Bragg peak"]{} % pos only allows for fractional value
node[pos=1.0, pin=above:"my custom label"]{} % pos only allows for fractional value
;
\end{axis}
\end{tikzpicture}
\end{document}
UPDATE: A slightly shorter version of the second solution in the answer by @Matthew Leingang:
\documentclass{standalone}
\usepackage{pgfplots}
\usepackage{pgfplotstable} % For \pgfplotstableread
\pgfplotsset{compat=1.10}
\pgfplotstableread{
0.01 1.00
0.011 2.00
0.012 3.00
0.013 4.00
0.05 5.00
}\datatable
% \pgfplotstableread{results.dat}\datatable
\pgfplotstablegetrowsof{\datatable}
\pgfmathsetmacro{\N}{\pgfplotsretval}
\begin{document}
\begin{tikzpicture}
\begin{axis}[ymin=0, ymax=6]
\addplot+[mark=none, forget plot] table {\datatable};
\addplot+[only marks] table {\datatable}
% pos = (index-1)/(N-1) (index starting from 1)
node[pos=(1-1)/(\N-1), pin=right:first point (1/\N)]{}
node[pos=(3-1)/(\N-1), pin=-45:third point (3/\N)]{}
node[pos=(4-1)/(\N-1), pin=-45:end of linear behaviour (4/\N)]{}
;
\end{axis}
\end{tikzpicture}
\end{document}