For drawing a torus, we can parametrize the surface as (for example)
x(t,s) = (2+cos(t))*cos(s+pi/2) y(t,s) = (2+cos(t))*sin(s+pi/2) z(t,s) = sin(t)
where both t and s take values on [0,2pi].
This code was written by cmhughes on TeX.SE.
\documentclass[border=5pt]{standalone}
\usepackage{pgfplots}
\pgfplotsset{width=7cm,compat=1.8}
\begin{document}
\begin{tikzpicture}
\begin{axis}
\addplot3[
surf,
colormap/cool,
samples=20,
domain=0:2*pi,
y domain=0:2*pi,
z buffer=sort
]
( {(2+cos(deg(x)))*cos(deg(y+pi/2))},
{(2+cos(deg(x)))*sin(deg(y+pi/2))},
{sin(deg(x))}
);
\end{axis}
\end{tikzpicture}
\end{document}