I've 2 web addresses say thinkingmonkey.me and thinkingmonkey.com have ip-address 127...1 (A.K.A localhost).

I wish to redirect any demands to thinkingmonkey.com to thinkingmonkey.me.

<VirtualHost *:80>
    ServerAdmin webmaster@dummy-host.example.com
    DocumentRoot /mysite
    ServerName thinkingmonkey.me
    ServerAlias www.thinkingmonkey.me
    ErrorLog logs/dummy-host.example.com-error_log
    CustomLog logs/dummy-host.example.com-access_log common
    Options -Indexes +FollowSymLinks
    RewriteEngine On

<VirtualHost *:80>
    ServerAdmin webmaster@dummy-host.example.com
    ServerName thinkingmonkey.com

    Redirect thinkingmonkey.com  http://thinkingmonkey.me/

  #  Redirect / http://thinkingmonkey.me/ #have even tried this

    ServerAlias www.thinkingmonkey.com
    RewriteEngine on

After I attempt to access thinkingmonkey.com the url doesn't get rerouted to thinkingmonkey.me. The url within the brower's address bar remains thinkingmonkey.com.

What shall we be held doing wrong?

mod_rewrite is recognized as better and much more effective to deal with these rewrites. You should use following code:

Options +FollowSymLinks -MultiViews
RewriteEngine on

RewriteCond %{HTTP_HOST} ^(.*\.)?thinkingmonkey\.com$ [NC]
RewriteRule ^ http://%1thinkingmonkey.me%{REQUEST_URI} [L,R=301]

Should you really-actually want to use mod_aias place the this line in VirtualHost portion of thinkingmonkey.com:

Redirect 301 / http://thinkingmonkey.me/

Do this:

RewriteEngine On
RewriteCond %{HTTP_HOST} !.*thinkingmonkey\.me$
RewriteRule ^/(.*)$ http://thinkingmonkey.me/$1 [R]

The documentation: http://httpd.apache.org/docs/2.2/mod/mod_rewrite.html