A current or recent threads would be nice once you’ve logged in so you can quickly see which your posts has been responded to without having to trawl through the entire site.
The “View new posts” button, duh. But maybe a similar list but showing only the threads you’ve participated in.
“View your posts” actually brings up threads you’ve participated in and the threads with newest posts come to the top. I find that feature very useful.
I almost always have View active topics open (“Display posts from previous” set to 7 days), and keep track of it that way 
Ditto “View Active Topics” (which is right next to “View New Topics” as a link–though only on the board index! Is there some way to migrate those links to the top of every page like “View Your Posts” Alex-or-Auggy??)
It shows me which threads have activity I haven’t read yet (and which threads haven’t had new activity since I checked on them!), and sorts them in descending order of post time from newest to oldest.
I practically never use “View your posts”. But I could see that being helpful, too.
“View New Topics” seems redundant, although I suppose it’s possible for a new topic to be swamped down the list of active topics.