1-3, I’d loudly ask if anyone else had intentions for it. For 4 (which I’m assuming is a pot luck or a picnic or a catered event or something like that), I just grab for the goal.
To me, 5. seems to be the most interesting question: how many people, upon being asked if anyone had designs on the last donut by an interested party, would scream “Hell yes!” and dive for it, body slamming the would-be muncher aside?
Or, how often are askers disappointed when someone offers to split it with you (“NO! I want the whole damn thing to myself or nothing at all!”)
I agree, the Last Lonely Half (or quarter) is hilarious in its pathetic-ness. 
I had to laugh when I got to the office this morning. On top of the microwave was a large box holding - you know what’s coming here - one dried-out, stale slice of cake. Yesterday afternoon was the going-away for one of our senior engineers. Apparently, it’s my piece, since I left before the cake was brought out.
You’d’a thunk they’d’a wrapped it up…
Last night, I asked my spousal unit about food in his office, since he’s often commented on the quantity of stuff people bring in to share. He claims the “last donut” syndrome doesn’t exist there. I guess NASA contractors aren’t shy about cleaning the plate.
Do you know a guy named Homer by any chance 
How in the world did you work with Jim Wilkinson? He’s still here; must be his doppelganger!
Same thing here, even though the garbage can can’t be more than six feet from the table, and even leaving a big box un-broken-down on top of it counts as throwing it out.
If people have had sufficient time to get a donut if they want it, I won’t hesitate to go for the last one. If I know the other folks well, the grab might even be accompanied by a loud “Yoink!”
At work, I’ll have the last one without asking; at the other places, I’ll ask if someone wants to share it with me.
I don’t usually run into this problem outside of work. At work I am always hesitant to ask because it makes me look like a glutton, and if anyone else really does want the last one I don’t want to feel guilty by making them feel obliged to yield to my wishes. If, after five to ten minutes, nobody else has snagged it and I really want it I’ll take it.
If it’s cold (e.g. pizza) or stale I don’t even want it at that point. Let someone else take it.
That happened a few years ago when I brought in homemade Christmas cookies for my office mates. No one wanted to be rude and take the last cookie, so the final cookie kept getting smaller, and smaller, and smaller.
Jahdra:
IIRC, there was a Dilbert strip on this subject once, in which the item in question is referred to as “Zeno’s donut.”
There’s a logical problem to the idea that it’s impolite to take the last donut. If everyone agrees not to take this donut, then the second-last donut is the real last donut, which means it would be impolite to take it, so no one will. But that means that the third-last donut is the real last donut…
The obvious conclusion is that it is impolite to eat any donut, and that they should just be given to someone for disposal. I volunteer.