You can use [yshift=<distance>] to offset your arrows. This will only work if you specify a node anchor (so for instance something like ([yshift=1ex]A.center)).
Here's your example with shifted arrows. Note that I removed the empty nodes you created with node {}, they're not necessary for drawing the arrows:

\documentclass[10pt]{article}
\usepackage{tikz}
\usetikzlibrary{automata,arrows}
\begin{document}
\begin{tikzpicture}[->,>=stealth',shorten >=1pt,auto,node distance=1.5cm,semithick,font=\tiny]
\tikzstyle{every state}=[fill=none,draw=black,text=black, text centered, text width=0.5cm]
\node[state] (A) {G};
\node[state] (B) [right of=A] {B};
\path ([yshift=1ex]A.east) edge ([yshift=1ex]B.west);
\path ([yshift=-1ex]B.west) edge ([yshift=-1ex]A.east);
\end{tikzpicture}
\end{document}
If you want the arrows to start on the edge, you could use the A.<angle> anchors, which specify points on the edge of your nodes, with A.0 being the right-hand edge, A.90 the top, and so on. I would also use the \draw (...) -- (...); syntax for drawing the arrows in this case, since it's more compact and you don't need the edge notation here.

\documentclass[10pt]{article}
\usepackage{tikz}
\usetikzlibrary{automata,arrows}
\begin{document}
\begin{tikzpicture}[->,>=stealth',shorten >=1pt,auto,node distance=1.5cm,semithick,font=\tiny]
\tikzstyle{every state}=[fill=none,draw=black,text=black, text centered, text width=0.5cm]
\node[state] (A) {G};
\node[state] (B) [right of=A] {B};
\draw (A.-25) -- (B.205);
\draw (B.-205) -- (A.25);
\end{tikzpicture}
\end{document}
[yshift=...]in your coordinates). If that doesn't answer your question, let us know. – Jake Nov 18 '11 at 06:34\path (B) edge node[yshift=10mm]{} (A);doesn't want to work, although I don't think that's the right syntax. – Concept Nov 18 '11 at 07:29tikzpicture. This ensure that all libraries as included and allows people to simply copy & paste your code, in order to test their solutions. – Martin Scharrer Nov 18 '11 at 08:08\draw ([yshift=2pt] A.east) -- ([yshift=2pt] B.west);and then a negative shift on the second line. Note that, even though this works fine for rectangles, it causes problems for nodes where the contact edge is not straight. Since this just puts the line at a vertical offset from thewestandeastanchors and won't account for the shape, it won't stay on the border. It is a mystery to me why you have an empty node at the edge by the way. – Roelof Spijker Nov 18 '11 at 08:35