The key hide y axis completely disables all ticks and lines, extra or otherwise. Instead, you can stop the axis line from being drawn by setting
separate axis lines,
y axis line style= { draw opacity=0 }
The separate axis lines is necessary to be able to assign the line style only to the y axis, since usually the axes are drawn with a single path. Note that you have to use draw opacity=0 to hide the y axis, the usual approach draw=none doesn't work here.

\documentclass{standalone}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
domain=0:360,
ytick=0,
separate axis lines,
y axis line style= { draw opacity=0 },
ymajorgrids,
tick pos = left
]
\addplot {sin(x)};
\end{axis}
\end{tikzpicture}
\end{document}
In case you want to do away with the tick mark and the tick label, the easiest thing might be to use one of the approaches from How can I add a zero line to a plot? to draw the zero line without the tick/grid mechanism.

\documentclass[border=5mm]{standalone}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
domain=0:360,
hide y axis,
before end axis/.code={
\draw [/pgfplots/every axis grid] ({rel axis cs:0,0}|-{axis cs:0,0}) -- ({rel axis cs:1,0}|-{axis cs:0,0});
},
axis lines*=left
]
\addplot {sin(x)};
\end{axis}
\end{tikzpicture}
\end{document}
major tick length=0pt, but that would apply to the x axis as well. I've edited my answer to show a different approach. – Jake Jul 31 '13 at 18:00gray, very thinorgray, ultra thin? – gypaetus Jul 31 '13 at 19:34thin,black!25. You can also use the actual style that's used to draw the grid lines by adding/pgfplots/every axis gridto the\drawoptions. – Jake Jul 31 '13 at 20:10y axis line style={draw=none}works fine. – Stefan Pinnow Jan 10 '16 at 06:57x=2000. – Diaa Apr 06 '17 at 20:16