How to plot functions like ‎‎‎‎‎x=f(y)‎‎ using TikZ?

\documentclass[tikz]{standalone}
\usepackage{tikz}

\begin{document}    
\begin{tikzpicture}
  \draw[->] (-3, 0) -- (4.2, 0) node[right] {$x$};
  \draw[->] (0, -3) -- (0, 4.2) node[above] {$y$};
  \draw[scale=0.5, domain=-3:3, smooth, variable=\x, blue] plot ({\x}, {\x*\x});
  \draw[scale=0.5, domain=-3:3, smooth, variable=\y, red]  plot ({\y*\y}, {\y});
\end{tikzpicture}
\end{document}

I agree that parametric is the way to go, but one really should be using pgfplots for this kind of thing:

Code:

\documentclass[border=2pt]{standalone}
\usepackage{pgfplots}

\begin{document}
\begin{tikzpicture}
\begin{axis}[xmax=9,ymax=9, samples=50]
  \addplot[blue, ultra thick] (x,x*x);
  \addplot[red,  ultra thick] (x*x,x);
\end{axis}
\end{tikzpicture}
\end{document}

This will work with the gnuplot backend.

\documentclass[tikz]{standalone}
\begin{document}
\begin{tikzpicture}
  \tikzset{swapaxes/.style = {rotate=90,yscale=-1}}
  \draw[red] plot[samples=200,domain=-1:2] function {x**2};
  \draw[blue,swapaxes] plot[samples=200,domain=-1:2] function {x**2};
\end{tikzpicture}
\end{document}