I’ll go first…The Office.
Now I know the two shows are fundamentally quite different, but they adapted what was already a very successful show, and turned It into an event more successfully one that lasted for significantly longer than the original did. I say that’s a win for them.
Anything else? Life on Mars, Being Human, The Inbetweeners…?
In the '70s there were several US adaptations of UK shows which were quite successful. All In The Family was based on Til Death Us Do Part, Sanford and Son was based on Steptoe and Son, and Three’s Company was based on Man About The House. In these cases both versions were very successful in their own ways.