How to get a more Linux like experience on Android? Are there projects (e.g. ROMs) out there that offers a more Linux like experience on Android?

Here are some things that I hope for


easy installation on similar platforms 
shell access
development tools such as gcc, Python
There are quite a few options already:


Chroot to a full fledged linux (search for debian chroot android, it's got quite a few hits)
There are also native ports of Debian or Ubuntu for some phone/tablet models.
Shell access is already there: Terminal Emulator
If you install an aftermarket firmware such as CyanogenMod you will get  root access, busybox, bash, an ssh client/server amongst other things
Here's the SL4A project (scripting layer for android), it adds python, lua, perl and other interpreted languages to android
You can build Qt applications (yes, even those using QtGui) using Necessitas -- a port of most parts of the Qt Desktop framework to Android. Applications as complex as Quassel (an IRC client/server) can be built with very minimal source changes. In theory this would allow you to build much of KDE4, though some parts (e.g. the Plasma workspace) may be too heavily tied to Xorg/GLX.
Most C/C++ programs from GNU/Linux that do not require a graphical interface can be compiled to run on Android using the Android NDK


You can also use Qpython3 for python in android .
Features:

Run Python3 applications including script
and projects on Android device
Execute Python3 Code &amp; File From QRCode
Support SL4A Programming, can access
android's feature, like network, bluetooth,
location
Support Python3 console
Support QEdit which allow you edit Python
code
Support FTP server, which can let you
transfer the Python3 project from your PC to
mobile easily


You can use kbox for linux utilities on your non-rooted android device.
Expand the Linux Capabilities on Android video shows how to install busybox without root.

Other things, you aware of. Feel free to add it here