I have a Tomcat6 server on a Linux server. The structure of the webapps directory is:
webapps
Delete ROOT folder, rename MyProject.war to ROOT.war and restart.
ROOT
MyProject.war
ROOT.war
You can also do it by adding the following line to inside the <Host> entry of /conf/server.xml
<Host>
/conf/server.xml
<Context docBase="MyProject" path="" />