I needed the same thing, but had things in the cells of the grid, which I also wanted to fade out. This solution is perhaps less elegant than others, but permits this sort of fading.
It just puts fading rectangles over the edges so they fade out to white.
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{fadings}
\begin{document}
\begin{tikzpicture}
\draw[step=0.5cm] (0.1,0.1) grid (3.9,3.9);
% Some letters to demonstrate fading
\node at (0.25,0.25) {F};
\node at (0.75,0.75) {A};
\node at (1.25,0.25) {D};
\node at (1.75,0.75) {E};
\begin{scope}[transparency group]
% Left edge
\fill[path fading=east, color=white] (0,0) rectangle (1,4);
% Bottom edge
\fill[path fading=north, color=white] (0,0) rectangle (4,1);
% Right edge
\fill[path fading=west, color=white] (3,0) rectangle (4,4);
% Top edge
\fill[path fading=south, color=white] (0,3) rectangle (4,4);
\end{scope}
\end{tikzpicture}
\end{document}

help lines
instead ofcolor=gray
– Leo Liu Nov 25 '11 at 19:25