Well, with all these NSA revelations it had to happen. Not only that Google is thinking about easing encryption in GMail but we got a pretty nice early code drop in a form of a Google Chrome extension.
Extension is called End-To-End and it will help you use OpenPGP encryption for your e-mails. Since it is a really early code drop, Google intentionally made it a bit difficult to install. First of all, you'll need to compile thing yourself.
sudo apt-get install git
sudo apt-get install subversion
After going through all steps, the extension is ready for deployment under
Load unpacked extension. I all went good you will see an additional icon next to the address bar.
Click on that icon will allow you access to Options where you can import key if you already have one (RSA or ECDSA). If you don't have a key, you can provide your e-mail have one created (only ECDSA). From that moment on you can create a new message by clicking that same magical button.
Currently extension is not really polished. Sending mail still requires a few manual steps, e.g. opening mail window yourself, decryption is not automatic, there is no public key lookup... but this is still probably best solution I have seen for a web mail. Best of all, it works with essentially any web mail - not just GMail.
While there is still a lot of work remaining to make this a comfortable solution, first steps are promising. Mail encryption is a bit hard by design but I could see myself explaining all necessary steps to someone with basic computer knowledge and having them send encrypted e-mail within minutes. To me that means that biggest issue is resolved. All other stuff is just an icing on the cake.
P.S. Those who don't have a Linux machine (or don't want to deal with compile) can download unpacked extension here. But do notice that this extension is alpha and I probably won't bother updating these binaries as the source gets updates.
[2014-12-17: Project source is now available on GitHub.]