2011 Xperias models ROOT,Ice Cream Sandwich (4.0.3, 4.0.4) (4.1.B.0.587 4.1.B.0.431 4.1.A.0.562) This is the new method to root

Supported phones = Xperia Arc S , Arc and Ray , Neo V, Neo, Live with walkman, Mini, Mini Pro, Active, Neo L, Xperia Pro

     Go to settings > Security > Mark  "Unknown sources"

     Settings > Developer options > Mark USB debugging

     Settings > Xperia > connectivity > USB connection mode > select MSC mode

     PC Companion installed on your PC

1. After marking the settings above, connect your phone to PC ( Skip PC Companion installation on your phone ) and wait for the adb drivers to be installed.
2. Download this rooting toolkit. Link > 1 / 2 / 3 / 4 and run it. If after running toolkit any download begins, cancel it by clicking on the green button. Don't let the eroot download anything. It should now detect your phone and show an option to "root". Just click on it, wait till it finishes.
3. Rooting done ( For confirmation see if any Super User app has been installed on your phone )

If it somehow fails for the first time, give it another go. Restart everything, your PC, phones etc. If it doesn't work at all, see the other method to root i;e Archived method to root 2011 Xperias below the animated Xperia Picture.