If you’re remoting in to a Windows box from a Mac, and using a (fullsize) Mac keyboard, you can accidentally get stuck in overwrite mode (instead of the normal insert mode) when entering text.
This happens because the Mac keyboard does not have a dedicated INSERT button like Windows keyboards do.
The solution is to press CLEAR on the OSX numberpad until you’re sure NUMLOCK is OFF (i.e. you press the numberpad buttons and the cursor moves instead of numbers appearing). Then, you can press the 0 key, which serves as an INSERT replacement (but only when NUMLOCK is off!), to get your cursor back to INSERT mode.
See here for more information about NUMLOCK on a Mac keyboard.
Bless you!