On Android: not directly.*but* You can run whole Linux distro on Android in light-weight virtualization (chroot).
My friends runs whole Debian-ARM on rooted Android in chroot and access the VM using VNC, so he has full-scale Linux desktop applications on his phone. It works best with pen stylus (on Galaxy Note) or with desktop-class display (20"+; via MHL cable) and keyboard.
It can also be done on convertible tablets (aka ASUS transformer). Basically what happens is that Debian Linux and Android share the same Android-Linux kernel and use Android drivers, that come with your
device, but have 2 different operating systems (userspaces) on top of a single Linux kernel. "chroot" feels like virtualization (VMware/VirtualBox), but it is more light-weight type.
The reverse is also true: if you have a Windows PC and wanna virtual Android: there is a "blue-stacks", that emulate an Android tablet on Windows PC.
Credit : http://tech.queryhome.com/251/running-a-linux-application-on-android-plateform?show=267#a267