Don't do it. You won't fail, I've heard stories of students white-outing entire essays or whatever and not failing (but also not doing well). It's likely that either:
a) it will be confiscated by a supervisor; or
b) it will be a huge waste of time.
I remember in year 12 I was told to scribble differently on exams. My normal method was to keep going over the words so that they become illegible and I was told that this was too much of a waste of time, and to just put a line through it. Now, if scribbling is supposed to be a waste of time, so must be the process of putting down your pen, picking up the white-out tape, getting the white-out tape to actually work, whiting out whatever you need, putting the tape back down, and picking up your pen again.
If it turns out you make a mistake and it costs you a lot of room on your exam, you can always request a script book or you can write in a different blank space on the paper (just make sure the examiner is clear about where your answer actually is!)
Also, when you correct things, say in a written exam, you can just use ^ or v and insert whatever word you wanted to be in there, or write above the word. It's fairly common, it won't effect your mark, it won't make you look like a retard (OMG!! That kid made a minor grammatical error under very stressful conditions, UG!!!), examiners are used to it, and you wouldn't have to re-write entire paragraphs because of a couple of errors. And like dekoyl said, it can be a good idea to only write on every second line.