On with the show.
As far as LEGO male parts go there are a few different sizes. The biggest would be the technic pin and axle at 4.8mm in diameter. It's use is widely known in technic applications as well as those builders who like to jam studs (which are also 4.8mm diameter) into technic pin holes.
Then there is the bar. A bar could be considered anything that will fit in a clip such as a minifig hand. The bar is 3.2mm in diameter and can be inserted into hollow studs. There is a wheels holder pin which is also 3.2mm but whose end is flanged and slotted for wheels to be able to pop on and off. This doesn't always have the same effect but can be used to some extent.
Finally there is the mini-pin which Bricklink also refers to as a pin in order to confuse us. This mini-pin is primarily used for minifig headgear accessories. Therefore you would expect that it would only fit into minifig headgear. But the case is not so. Some of the more enlightened individuals out there will also remember the older taps which actually had holes in the end of them. Clever folks would put a trans-blue plume in them to make it look like water was gushing out. Or other colors for things that you might not expect coming out of taps. Yellow for custard?
The mini-pin is approximately 1.6mm in diameter. This is the same thickness as baseplates or the half-plate element of brackets. But where else can we find a 1.6mm hole? Look no further than your local 1x plate. Extend your hand. Now grab the plate. Flip it over. Is it a boy or girl? Depends. What does the bar underneath look like? Is there a hole in the middle? That hole is an ingenious idea by LEGO to maintain structural integrity of the part while also saving a fraction of a gram of ABS. Multiply that fraction of a gram over millions of parts and you get a few truckloads of savings per year.
Even more ingeniouser is the fact that this mini-pin hole is not just some random size. No, it is highly refined by it's creator to be something exquisite that works with the system in which it was intended to be used. That hole is the perfect size to fit the mini-pin. Try it. Go ahead, I'll wait. Isn't that amazing?
What'd I miss? Where else can the mini-pin fit? Flaming apple bomb anyone?