If you glance up to the address bar, you will see that this post is being served securely. I've done this because I believe strongly in the importance of internet privacy, and I support the Reset The Net campaign to encrypt the web.
I've done this completely for free. Here's how:
Get a free certificate
StartSSL isn't the nicest website in the world to use. However, they will give you a free certificate without too much hassle. Click "Sign up" and follow the instructions.
Get an OpenShift Bronze account
Sign up to a RedHat OpenShift Bronze account. Although this account is free to use, as long as you only use one 1-3 gears, it does require you to provide card details.
Once you have an account, create a new application. On the application screen, open the list of domain aliases by clicking on the aliases link (might say "change"):
Edit your selected domain name and upload the certificate, chain file and private key. NB: Make sure you upload the chain file. If the chain file isn't uploaded initially it may not register later on.
Pushing your site
Now you can push any website to the created application and it should be securely hosted.
Given that you only get 1-3 gears for free, if you have a static site, it's more likely to handle high load. For instance, this site gets about 250 visitors a day and runs perfectly fine on the free resources from OpenShift.