Can you hide a thread from appearing in a forum thread list widget?

There is no way to hide a single thread. If its useful information you may consider capturing it to a wiki page or other medium and control access there.

Is there a way with the API?  For example if we wanted to show a list of latest threads on our main website, but exclude anything with a particular tag?  If not, let me know and I'll make an idea for it.  Over the years across different community platforms I've seen where that would be useful.

The tags api does not really exclude by tag, it only filters to specific tags.  You could potentially do a search query to exclude by tag, but then you are not looking at a thread anymore, rather a search result that is not a full representation of the thread, so you will lose some information unless you re-get the thread each time.  t also means a complete custom UI which is more complicated.

Hi Patrick.  Thanks for the confirmation.  I created an idea for this here:

https://community.telligent.com/community/i/ideas_and_improvements/ability-to-exclude-content-with-a-particular-tag-from-widgets-and-apis

EllenB Alex Nassi - Please vote this up if it is something you would like to see too.

Thanks Matt Nevill, that's great. I'll go in and vote it up now! This would be really helpful for us. 

An option...if those who use it can be limited by security role...

1.  Create a second forum in the group and adjust the permissions so that only the users you want can read it.
2.  If you don't want new posts in that forum adjust permissions accordingly as well.
3.  Move the thread in question to that forum and potentially lock it to future replies
4.  On the thread list page add a second thread list and scope it to your new forum

The new threadlist will only show the thread to those with permission to view and it will no longer be in the other one.  Its a bit cumbersome but an option that requires no special code if its an important thing to do.