My preference would be for the image not to show up at all on most AJAX actions unless it is something expected to take a long time, such as validating and submitting a form or indeed something as intensive as a cache rebuild.
I like it appearing even on things such as a like. If it's a site that loads slow, that may take a second. Having a link that doesn't immediately do anything would make me think the site is dysfunctional. I realize that without that appearing, when I click like and it's done loading it changes to 'unlike' and shows a new div (the likes summary) but still, on a delay it could seem like it's broken.
That said, it is pretty easy to disable, I think it's just a matter of including global: false in the arguments for the ajax request.
I personally like it showing up, even if for a split second. It makes it completely obvious that "Hey, this page is doing something via Ajax". It might just be me and the fact that 90% of the time when I'm on here I'm downloading something, so my Internet is slow and warnts the image being displayed.
Exactly my point. I'm not fortunate enough to have Fios, and my Internet is usually always tied up in updates - which means pages take about 2-6 seconds to load, the Ajax indicator lets me know my request is still processing.
Not to mention the amount of people who do still have dialup or satellite Internet.