Wubi shows " Ubuntu needs atleast 256 mb ram to install the GUI." I have ASUS P4 256 MB computer. 8 mb ram is consumed by graphics. So in all i have 248 mb ram. But they say that ubuntu can run with less than 256 mb ram. So whats the problem. No doubt the installation still proceeds and after restart on booting into ubuntu, the screen loads but after some time a dialog box pops up saying "Unrecoverable error. System needs to shutdown". Please suggest a solution.

256 mb are requred to install, but how much to run?

better try distro like debian, crouchbang, etc..

What if i try the older versions of ubuntu?

Correct, that means that Wubi needs a minimum of 256 mb ram to get the GUI installed.

Maybe not Ubuntu, but a more lightweight distro like DSL (Damn Small Linux) or Puppy Linux can. Ubuntu requires at least 256 mb ram to even get installed

The answer to your problem can be found in your very own topic here:
You have 256 mb ram installed. You're using Windows XP which needs a minimum of 64 mb ram, recommended 128 mb ram. Then your graphic card is using 8 mb ram:
256 - 64 - 8 = 184 mb ram left (minimum amount ram XP).
256 - 128 - 8 = 120 mb ram left (recommended amount ram XP).

Under XP i guess you're running an anti-virus tool, a firewall which also consumes resources, maybe more tools and programs running in the background (check your taskmanager). So, my best guess is that the amount of ram left to install Ubuntu must between 0 mb and 120 mb ram. Not enough for Ubuntu. And even Wubi uses resources to run!

How large is your hard disc? Maybe it is better to create a dual-boot system. Or you might get some more ram in your system. But running Ubuntu this way will keep providing you nothing more then problems.