Of those, astronomy of course offers some of the most dramatic examples of scale and the biggest challenges to our human-centric impression of the universe. A lot of these are on such a huge scale that it's hard for us as mere apes to really understand the ramifications. However, I came across the video below the other day, and thought it was a nice example of a common misunderstanding of scale that's a little closer to home.
If you'll humor me, make a circle with one hand to represent the Earth and then use your thumbnail on your other hand as a stand-in for our moon. If your thumbnail is about 0.5 inches wide, then you should make your "Earth" about 2 inches from pole to pole. Now, hold your hands apart at a distance that you think accurately represents the distance from the Earth to the moon. If my math is correct* then you're on the money if you're holding your hands about four and a half feet apart. If you were way off, you're not alone, as the video below demonstrates:
You can just ignore the bits after about 1:20 in. The comparisons he starts to draw aren't really that clear or compelling, and as the folks in the comments have made aggressively clear, the bit in his slide where the light distance to the nearest star is multiplied by the number of stars in the galaxy is all sorts of wonky (first of all, it doesn't make any sense to multiply those two values, and secondly most current estimates of the number of stars in our galaxy lean toward 400 billion rather than 100 billion).
Misgivings about the end of the video aside, hopefully the distance he had to walk away (and the distance you had to hold your hands apart) helped your concept of distances in space, either by giving you a handy (lololololol) model for the distance if you were already aware of it, or by giving you one of those lovely little moments of sudden awareness if you weren't.
And if you're an easily entertained doofus like me who sent your thumbnail moon crashing into your Earth hand in a life-obliterating cataclysm, then you're welcome for the extra 30 seconds of apocalyptic fun.
*That can be quite an assumption given that my brain is allergic to numbers. But here's how I got it: moon's diameter ~2,160 miles, average distance from moon to Earth ~239,000 miles. If your thumbnail is 0.5 inches, then that's about 4,320 miles to the inch. So 239,000 miles divided by 4,320 miles/inch = 55.4 inches = 4.61 feet. Also, diameter of the Earth ~8,000 miles, so about 2 inches. That's a whole bunch of rounding, so the distance in inches is by no means exact, but a decent approximation, I think. If there's a problem with my values or arithmetic, please let me know.