Click on a tag and you get "N questions tagged TAG1 TAG2....". Could those tag buttons please have an 'x' by them, like the ones on Interesting tags? It's easy to add another tag to your search by clicking another tag button, but not to remove one.
I'll post a few screenshots so this answer is more colorful and fluffy and upvote-inviting.
Click these "remove tag" buttons to hide all questions with the given tag:
Also works on the tags in the sidebar:
Settings are persisted via
localStorage! Clear them with this cute glossy button:
It was tested under stable versions of Chrome, Firefox and Opera, on Windows and on Linux.
Wouldn't guess what happens if ran on MSIE (but for that matter, a toaster doesn't run it either...).
Also note that this is just a proof of concept (by this I mean that it may not be ideal for daily usage; also, it could fit better to the look of the site and all).
As a workaround, you can remove all tags from your search by pressing "Questions"