Is there a notepad-like app with no toolbars, menus or an ability to save? We have this special requirement for this kind of tool. I saw an app fitting this exact description a couple of years back but I can't remember what it's called. I've been googling for an hour to no avail. :)
As the comments have already pointed out, most software which allows users to enter data also allows for them to save their data.
Perhaps the best bet would be to create your own application with a large text field.
This tiny tutorial is already too in-depth for what you wish to achieve, but it's the lowest-level tutorial I could find on short notice :)