The spacing around the wrapfigure is given by two lengths: \columnsep (for horizontal padding) and \intextsep (for vertical padding). Here's an example illustrating the difference between the default and setting them all to 0pt:

\documentclass{article}
\usepackage{graphicx,lipsum,wrapfig}% http://ctan.org/pkg/{graphicx,lipsum,wrapfig}
\begin{document}
% Default settings
\begin{wrapfigure}{r}{0.5\textwidth}
\centering\includegraphics[width=\linewidth]{example-image-a}
\caption{Basic layout}
\end{wrapfigure}
\lipsum[1]
% Adjusted settings
\begingroup
\setlength{\intextsep}{0pt}%
\setlength{\columnsep}{0pt}%
\begin{wrapfigure}{r}{0.5\textwidth}
\centering\includegraphics[width=\linewidth]{example-image-a}
\caption{Basic layout}
\end{wrapfigure}
\lipsum[1]
\endgroup
\end{document}
The default for \columnsep is 10pt, while \intextsep is 12.0pt plus 2.0pt minus 2.0pt. The following is taken from the wrapfig documentation (section 2 Sizing and optional overhang, p 3):
LaTeX will wrap surrounding text around the figure, leaving a gap of \intextsep at
the top and bottom, and \columsep at the side, by producing a series of shortened text
lines beside the figure. The indentation (shortening) of the text is the figure width plus
\columnsep minus overhang (if any; see below).
LaTeX calculates the number of short lines needed based on the height of the figure and
the length \intextsep. You can override this guess by giving the first optional argument
(parameter #1) specifying the number of shortened lines (counting each displayed equation
as 3 lines). This is particularly useful when the surrounding text contains extra vertical
spacing that is not accounted for automatically.
So, barring that you don't have any whitespace around your actual image, you can also adjust \columnsep and \intextsep to your liking for any particular wrapfigure.
\begin{wrapfigure}{r}{*insert number here* \textwidth}– Razor Apr 29 '13 at 17:30