Can I stop seeing updates from 'Show new replies to your posts'?

[proteus]

Unfortunately, no.  The version of the Forum software we use does not have a way to "unfollow" a thread you've participated in. The 2.0 version does have a mod which allows this -- but SMF 2.0 breaks the theme.

At some point, proteus will have time to port the theme to SMF 2.0, and everyone will be much happier. For now, though, we're all out of luck.

[von Corax]

We're now running SMF 2.0, which means that it is now possible to unfollow threads. Under "Profile -> Account Settings", go to "Modify Profile -> Notifications", where you will see a list of threads and boards for which you are receiving notifications; here you can cancel any of your notifications. Also, when you click the "Notify" button on a thread, it will change to "Unnotify"; clicking that button will disable notifications for that thread.