Debian Kit for Android
sven-ola.dyndns.org
sven-ola.dyndns.org
https://play.google.com/store/apps/details?id=ru.meefik.linu...
The problem with recent Android is that most apps require the full system with all the services / contentproviders. You can download the playstore APK or individuals APK if you wish.
The second option is to run the x86 version of Android in a VM or chroot + VNC (linux only). Apps using the NDK wont run, but you will get native-ish speed for the apps that does run. As for an "integration mode" where many apps can run in parallel with their own WM client, I don't think there is something for that yet.
AFAICT the linux system is fully functional (native performance, latest browsers etc should work fine?), but unaware of android's presence. What is holding us back from doing the whole ubuntu-for-android-esq experience? - ie, linux boots when HDMI connected, android then lives inside an app in linux, and android notifications are shared to the desktop linux? and no RDP limitations. FYI this system is available to users of motorola phones of a certain age (atrix-d.razr)[1], with issues (at least the ubuntu version i tried; old ubuntu and unable to install eg. the latest browser versions).
The polished version of concurrent linux+android has massive potential, IMO.. although this looks like a good step forward, subject to ubuntu still not releasing anything of their u4a!
1. ubuntu: http://forum.xda-developers.com/showthread.php?t=1281528 gentoo: http://forum.xda-developers.com/showthread.php?t=1617684
http://the.taoofmac.com/space/blog/2013/02/10/1230#an-arm-on...
Note that the guy got Ubuntu 12.04 running on an ODROID board using a similar technique from a prebuilt image. So it's apparently a very easy thing to get going...