3 equations + vertical dots

I think you can simplify a bit and use something like this (from the amsmath package):

\begin{align}
   x_{0} &= y + m_{0} \\
   x_{1} &= y + m_{1} \\
   &\;\;\vdots \notag \\
   x_{n} &= y + m_{n}
\end{align}

The notag command removes the equation numbering from the line with the vertical dots. I am sure there is a way of adding the exact amount of white space (equal to half the width of the equals sign) to center the dots under the =, but this does the job in a rather simple manner.

EDIT (with inspiration from Manuel's comment)

The mathtools package provides two versions of the vdotswithin command (notice the missing \\ in the short version).

\begin{align}
   x_{0} &= y + m_{0} \\
   &\shortvdotswithin{=}
   x_{1} &= y + m_{1} \\
   &\vdotswithin{=} \notag \\
   x_{n} &= y + m_{n}
\end{align}

Resulting in:

You don't have to write the equation twice: you have to write the relation symbol w.r.t. which the dots will be centred. Illustration with \vdotswithin and \shortvdotswithin:

\documentclass{article}

\usepackage{mathtools}

\begin{document}

\begin{align}
  x_{0} & = y + m_{0} \\
  x_{1} & = y + m_{1} \\
        & \vdotswithin{ = }\notag \\
  x_{n} & = y + m_{n}
\end{align}

\begin{align}
  x_{0} & = y + m_{0} \\
  x_{1} & = y + m_{1} \\
        & \shortvdotswithin{ = }\notag \\[-3.5ex]
  x_{n} & = y + m_{n}
\end{align}

\end{document}