How do I define a right arrow with bar in LaTeX?

The stmaryrd font has \mapsfromchar:

\documentclass{article}
\usepackage{amsmath}
\usepackage{stmaryrd}

\newcommand{\Rightarrowbar}{\Rightarrow\mapsfromchar}
\newcommand{\Leftarrowbar}{\mapstochar\Leftarrow}

\begin{document}

$a\Rightarrowbar b$

$a\Leftarrowbar b$

\end{document}

If stmaryrd is not an option for you, it's possible to reflect \mapstochar:

\documentclass{article}
\usepackage{amsmath}
\usepackage{graphicx}

\newcommand{\fakedmapsfromchar}{%
  \mathrel{\mathpalette\reflectmathchar\mapstochar}%
}
\makeatletter
\newcommand{\reflectmathchar}[2]{%
  \reflectbox{$\m@th#1#2$}%
}
\makeatother

\newcommand{\Rightarrowbar}{\Rightarrow\fakedmapsfromchar}
\newcommand{\Leftarrowbar}{\mapstochar\Leftarrow}

\begin{document}

$a\Rightarrowbar b$

$a\Leftarrowbar b$

\end{document}

Something like this?

\documentclass{article}
\usepackage{mathtools}

\newcommand{\myRightarrow}{\mathrel{{\Longrightarrow}\!\vcenter{\hbox{$\scriptscriptstyle|$}}}}

\begin{document}

$ A \myRightarrow B$

\end{document} 

Edit: If you want the final bar to have the same width as the \Rightarrow, you can use two consecutive | with some kerning between them:

\newcommand{\myvarRightarrow}{\mathrel{{ =⇒ }\!\vcenter{\hbox{$ \scriptscriptstyle|\mkern-5.4mu|$}}}}

One can always build a symbol by himself (thanks to samcarter, this is a scalable version):

\documentclass[margin=1mm]{standalone}
\usepackage{graphicx}
\usepackage{amssymb}
\newcommand{\yoursymbol}{\mathbin{\Rightarrow\hspace{-0.45em}\vcenter{\hbox{\scalebox{0.8}{$\shortmid$}}}}}
\begin{document}
$1\yoursymbol2$ {\Huge $1\yoursymbol2$}
\end{document}

Caution: This doesn't work in subscript. I'm trying to find some solution...