There are two steps to solve this problem. First, create a new route or change the default route to accept an additional parameter:
routes.MapRoute( "Default", // Route name
"{controller}/{action}/{id}/{ignoreThisBit}",
new { controller = "Home",
action = "Index",
id = "",
ignoreThisBit = ""} // Parameter defaults )
Now you can type whatever you want to at the end of your URI and the application will ignore it.
When you render the links, you need to add the "friendly" text:
<%= Html.ActionLink("Link text", "ActionName", "ControllerName",
new { id = 1234, ignoreThisBit="friendly-text-here" });