Remove unwanted ^M tags from file using vi

After I opened a file in gedit (under Gnome), and edited the file, this file contains now a lot of ^M-tags on the end of each line.

To remove these tags (using vi), I found this page, where a standard syntax for this kind of search and replace of special characters is explained.

This command is kind of tricky in that you have to type the Ctrl-V and Ctrl-M in sequence to receive the right command.