I'm definitely re-watcher. If there is a drama that I really enjoy to watch, why not watch it again? But I've only once started re-watching drama right after finishing it. But for example I've watched
You're beautiful 6 times and I'm sure I'm still going to watch it many times in the future.
In some dramas you can get more out of that drama if you watch it more than once. And it might be very interesting to watch drama that you've already seen because you know whats going to happen so you can watch it in other perspective.
But yes there is dramas that are "re-watchable" and those that are not.