Try the coordinate matrix transformation option cm=....
\documentclass{article}
\usepackage{tikz,tikz-3dplot}
\begin{document}
\begin{tikzpicture}[scale=3]
\draw[thick,->,black] (0,0,0) -- (2,0,0) node[anchor=north east]{$x$};
\draw[thick,->] (0,0,0) -- (0,1,0) node[anchor=north east]{$y$};
\draw[thick,->] (0,0,0) -- (0,0,1) node[anchor=east]{$z$};
\end{tikzpicture}
\begin{tikzpicture}[scale=3,cm={-1,-1,1,0,(0,0)},x=3.85mm,z=-1cm]
\draw[thick,->,black] (0,0,0) -- (1,0,0) node[anchor=north east]{$x$};
\draw[thick,->] (0,0,0) -- (0,2,0) node[anchor=north east]{$y$};
\draw[thick,->] (0,0,0) -- (0,0,1) node[anchor=east]{$z$};
\end{tikzpicture}
\end{document}
Edit: TikZ provides a coordinate transformation matrix cm = (a,b;c,d) that can be used to transform the coordinates (x,y) into a new set of coordinates (X,Y) = (a,b;c,d)*(x,y) = (ax+by;cx+dy). In the OP's case we want the direction of X to be 'towards you', i.e. X = -x - y. The Y coordinate must be 'to the right', i.e. Y = x. Solving for a, b, c and d we find
a = -1,
b = -1,
c = 1
d = 0
This is what is given in the option cm={a,b,c,d,(0,0)} where (0,0) is the x- and y-shift of the origo.
The new Z coordinate is Z = X + Y = -y.
Before being plotted, the coordinates are multiplied with the TikZ unit vectors. Default is x=1cm, y=1cm and z=-3.85mm. Thus to get the same length and direction of the axis in the new orientation we need to change this to x=3.85mm, y=1cm and z=-1cm. As y=1cm is the default this is left out.
I am not sure the above is clear... Feel free to improve the explanation.
tikz-3dplot. – Mikael Vejdemo-Johansson Apr 16 '11 at 16:57