The new Pi 3 was announced this morning. It's the first Pi to ship with a 64-bit processor, the ARM Cortex A53. The product page for that chip suggests that it's capable of hardware virtualization. Given that Raspbian is currently a 32-bit only environment, are there any virtualization programs that will run on Raspbian which will allow me to run 64-bit applications?
@jason.kaisersmith Docker won't work on the RaspberryPi (regardless of version) without some significant rework. The Docker site indicates that docker requires a 64-bit OS (https://docs.docker.com/engine/installation/linux/debian/).
Some work has been done to make it work on the pi (http://resin.io), though I'm still evaluating how well it actually works in practice.
To answer the specific questions asked, I've never encountered a virtualization engine that would allow you to emulate a higher bit OS/Architecture than was running on the host system. I don't believe that it is possible, and if it is possible, it would be terribly slow.
While not full virtualization, have you considered Dockker on pi?
Docker allows you to host containers, which are lightweight and offer a lot of flexibility. They have advantages (and disadvantages) when compared to full virtualization but depending on what you want to do they can be very flexible.
I've not tried docker on Pi, but do have it on my laptop and if you are somebody who likes to try new things and tinker then it's great.