Yes, although very clear that it is not a good practice to do that, I did it recently when installing lights for christmas. But when I do it I really conscient that I may fall and usually ask for somebody to help me. The real danger is when you are not aware of that and go on with too much confidence.
Assuming this is a step-ladder, This is a physics question and it's about centre of gravity. Stability is increased with a low centre of gravity and decreased as the COG is raised. When you stand on the top of the ladder, you are above the natural centre of gravity of the ladder and any movement you make increases instability. So it is undoubtedly dangerous.
If it is a ladder leaning against a wall, then it is about friction and force-vectors. Below the top rung, there is a downward force into the ground and a lateral force into the wall. When you stand on the top rung, there is no significant force into the wall. Your position up the ladder acts as a lever against the friction at the bottom; and if the friction at the base is at risk of giving away. The ladder will slide down the wall. This depends on the angle of the ladder to the wall so it's important to pick the best angle and don't use the top rung. Ideally, anchor the feet to the ground/tie the ladder to the wall.
On a step ladder I do if I can't reach something but I am quite quite nimble, have good reflexes and am "well balanced"!
Yes it is very dangerous to stand on the top rung of a ladder. On a ladder propped against a wall it would be difficult to even do this without falling backwards (unless the ladder leads to an open window or raised doorway). When standing on lower rungs, some of the treads or the stiles are in front of your chest or at least at waist level, so you can brace yourself against them. Ideally you shouldn't stand so high that the top rung is lower than your shoulders if there is nothing else to hold onto. If you stand on the upper rungs and lose your balance, the first thing you try to do is grab something - but there may be nothing there. If you are lucky, you may be near a wall and could stop yourself from falling. Some step ladders have a top platform for standing on but the safest ladders have a bar joining the two stiles which you can hold onto.
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