This seems to be one of the hundreds of things that Tab Mix Plus already does. Unfortunately it doesn\'t seem to work in Firefox 3 and I miss this Tab Mix Plus more than anything since I upgraded to FF3.
Very simple and does the trick. Most times I'd rather have a tab open relative, but sometimes on the right would be preferable. If you wanted to expand this one, a right-click context option to "Open Relative" or "Open Right" would be something to consider.
I have been looking for just this functionality, and it works as advertised. It would be nice if you could configure it to only open tabs directly to the right if it is a manually opened tab (as opposed to a link)