Works on ICS and Jelly Bean.
I don't recommend Method 1 anymore, please use Method 2 for all Note 10.1s!!!
[Method 1 - Root injection via ODIN stock firmware] [GT-N8000 and GT-N8013]
Root-injection method will give you just root and also does not increase the binary count. This is a good root method for those of you who just want root and also be able to receive firmware updates easily.
However, the official firmware downloads are near 1GB and currently not available for all firmwares (just European/Saudi/UnitedEmirates available) on GT-N8000. You can still install this on any GT-N8000 but you will have to change the firmware to the available ones.
See here: http://rootgalaxynote.com/galaxy-not...axy-note-10-1/
[Method 2 - ClockworkMod Recovery][GT-N8000, GT-N8010, and GT-N8013]
The ClockworkMod Recovery method installs CWM Recovery to the recovery partition to your GT-N8000 then you can simply flash a Superuser zip file to get root. This is the easiest method and also is easily restorable to stock and get OTA updates by flashing stock recovery over it. Also you can keep whatever firmware you have and download size is less than 20MB. Also, once you have CWM Recovery, you can install/restore/backup ROMs. If you are thinking about installing custom ROMs in the future, use this method.
See here: http://rootgalaxynote.com/galaxy-not...odcwmmethod-2/
UPDATE (8/16/2012 10:55AM PST): The CWM method works just fine on the Wifi version GT-N8013, just confirmed on my new Wifi Note 10.1, got it rooted within 5 minutes.
UPDATE (8/16/2012 4:20PM PST): Just added root-injected system image for GT-N8013, it will not increase ur binary count and give u root.