I have heard that there is some similarity in the code used for both Ubuntu and Android programs, but has there been any mention in all the recent publicity over the forthcoming Ubuntu OS for phones, whether or not existing Android apps will be compatible with Ubuntu?
So far, the Ubuntu QML toolkit is just a preview, so there is no definite answer possible. But Richard Collins, head of Ubuntu mobile products, has stated in an engadget interview:
Q: Since Android is also Linux-based, is there any plan for Ubuntu to run Android apps?
A: Many Android developers already use Ubuntu as their desktop OS and we have a very close affinity with them. We intend to encourage them to make their Android applications run on Ubuntu, but we won't engineer any middleware for running Android apps. Developers are intelligent and capable enough to make their apps run on our devices. We have an active initiative right now to directly help them achieve this.
So this makes it pretty clear: the apps should be either web apps or ported to Ubuntu.
It may be possible with OpenMobile's Application Compatibility Layer. They have already demonstrated it with Tizen OS and from its site, it is clear that it will be available for Ubuntu too.
Source: OpenMobile ACL for Ubuntu
As previously answered, canonical won't support android apps on ubuntu touch. Their official reasoning is that "native" apps are faster. A point they don't mention is that oracle draged google on a billionaire lawsuit for using java on android (google "google oracle java lawsui"t). It should be pretty simple for ubuntu to support android apps, but it would require the "dalvik vm" which might drag canonical in a lawsuit too big to make it all worth it. However, third parties can, and most probably will port dalvik to ubuntu in order to support android apps, I bet someone will do it right after the official ubuntu touch is released. The problem with all this is that it does not solve the problem of legally runnning apps bought for android. I don't think it should be a problem for free apps though.
I remember seeing this article a while back. You can run android apps using Google-Chrome with a few tweaks. I have not tried it myself. I found the link and others by googling "run android apps on ubuntu" http://www.omgubuntu.co.uk/2014/09/install-android-apps-ubuntu-archon