Is there a way to grate a block of cheese entirely without hurting one's fingers or knuckles? You know the scenario: You grate the cheddar until you're left with a quarter-inch. What do you do? Try to grate it and risk cutting your knuckles, or pop it in your mouth and enjoy?

Usually I do the latter, but I wondered if anyone has any tips for grating cheese down to the last bit?

Is there some kind of small tool that you can use to safely grate the last of a block?
By the wording of the question, I'm pretty sure you're using one of those pyramidal graters or a "sheet" grater.

That's great for getting the "bulk", but if you want to grate a small amount of cheese (or the last bit of a large amount, if you don't want to just eat it) then you really need to get yourself a rotary grater.  They're more commonly used for fine/hard cheeses such as Parmesan, but most half-decent ones will come with a "coarse" blade that can be used for cheddar, mozzarella and so on.

Rotary graters all have a plate at the top that lets you push the cheese down onto the blade.  Higher-quality graters will give you slightly better results; the $10 cheap ones tend to leave a mush at the bottom that's hard to grate, even if you squeeze really hard, but that's easily remedied with a small wooden block or really any object at all to put between the top plate and the cheese you're trying to grate.