Using HTTPS has several advantages over HTTP.
A big benefit is regarding the perception of security. As visitors become more aware of the little padlock thingy in their browser address bar they will begin to associate it with security and integrity. Sure, it doesn't mean your site is secure or the site is trustworthy but if it becomes a perception then there's no point kicking against the goads.
Another huge benefit is the effect it will have on search engine rankings. And we all know that means Google. If Google says you should be using it then you have no choice if you are serious about rankings.
If you are a site builder and are using a content management system like Joomla then you also need to be aware that just because your login box doesn't visually appear on the site doesn't mean Google's crawler bots won't pick it up. Publishing and presence are 2 different things with Joomla. You need to be checking your sitemaps and Google's page index of your sites to see if there's any presence of a 'login' function.