Within the College of Liberal Arts and Sciences, we've started the effort to move all of our websites to SSL. Put in another way, we were using http except for pages which specifically had highly secure or private data. Now we are moving toward using https on all pages of our websites.
While this may not be particularly exciting to the average user, it does provide some advantages to both the website user and the website owner.
For the user, visiting a website secured with SSL will provide a layer of browsing privacy. For the website owner, there will a bonus of increased search rankings and also site visitors will view using your site as a secure experience. Google has been advocating "SSL Everywhere" for some time, but will be or has already started affecting their search ranking algorithm and has ramped up their warnings to users of the Chrome browser when visiting a site which is not secure.
As an additional point with a secure website, there needs to be a certificate which needs to be valid.
- the certificate was issued for that domain name
- it came from a known certificate authority
- the certificate is being used within its valid date range (they have an expiration date)
The College of LAS takes care of SSL certificates used for the websites we hosts, but if you are hosting something on a departmental server or elsewhere, ACCC is where we request our certificates. They have a nice page detailing on ACCC support for SSL Certificates.
Here is more on the topic of Google's take on this.
As a user, your experience relating to secure websites will vary based on the browser you use. Here is an interesting article relating to user behavior and browser based warnings when a site is not completely secure.