EDIT: previously incorrectly stated 'url' instead of 'domain'.
EDIT: previously incorrectly stated 'url' instead of 'domain'.
Regarding security, using HTTPS (along with the right measures on externally-hosted content) guarantees (to some extend) that what the users gets is what you meant to publish: an hostile network cannot replace the content with misinformation and cannot inject JS -- to exploit the client or not (as was done with the “Great Cannon” [0] which took down Github).
Privacy-wise, a number of countries routinely spy on their communication infrastructure, and revealing “I visited this website” is far more problematic than “I visited this Tor-related post on this website, and left this comment”.
The last reason for systematic HTTPS is “political”: if we go towards a situation where HTTPS is systematically employed, HTTP-only website will be subjected to increasing amounts of social pressure as adoption rates grow: deploying HTTPS (and preferably best-practices) on your “text-only” website pushes other websites (that might “need” it more) to deploy it too.
A more frequent one is injection of ads or tracking scripts, or 'web accelerators' that recompress images. Certain ISPs have been known to do these.
/* insert ascii goatse here */
The only thing that's not hidden are the domain names in the certificate that the server presents.
The rest of the URL is encrypted, along with all data and headers.