Aligning at the equation tags
align* is not required if you just wish to align the items. Here's an example using multienum:
\documentclass{article}
\usepackage{multienum}
\renewcommand{\regularlisti}{\setcounter{multienumi}{0}%
\renewcommand{\labelenumi}%
{\addtocounter{multienumi}{1}\alph{multienumi})}}
\begin{document}
\begin{multienumerate}
\mitemxxx{\(x^2 + y^2 = 1\)}{\(a + b = c\)}{\(r-x = y+z\)}
\mitemxxx{\(f - y = z\)}{\(a - b = 2d\)}{\(r+x = 2y-3z\)}
\end{multienumerate}
\end{document}

Aligning relation symbols and equation tags
If you wish to align both at relation symbols and on equation numbers, I recommend to use the alignat* environment. Mark alignment points by &, further use & to separate columns. The argument to alignat* specifies the number of columns. Here we've got six columns: three for the tags and three for the equations.
\documentclass{article}
\usepackage{amsmath}
\newcounter{eqn}
\renewcommand*{\theeqn}{\alph{eqn})}
\newcommand{\num}{\refstepcounter{eqn}\text{\theeqn}\quad}
\begin{document}
\begin{alignat*}{6}
\num&& x^2 + y^2 &= 1 \qquad& \num&& a + b &= c
& \num&& r-x &= y+z \\
\num&\quad& f - y &= z & \num&& a - b &= 2d
\qquad& \num&& r+x &= 2y-3z
\end{alignat*}
\end{document}

I used automatic numbering. You could do it manually as well, just take care of the font, the tags should be in text font. So they don't look like variables.
subequationsenvironment from amsmath. – Andrey Vihrov Mar 06 '11 at 14:59