LOL! Deffinately a weird thread... There are some real weird ones on here mind you
Anyways, I can offer some limmited explenations... The fish that go up and down are bored/frustrated/stressed and that may be a sign that they are crowded, distressed in some way or simply lacking stimulation. re-arange their tank a bit, feed them something different, check your water params., do a water change and/or re-think your stocking.
Those of you mentioning fish that 'pace' back and forth - that's territorial and also due to boredome. It's completely typical of bettas which tend to be kept in very small understimulating tanks and also are highly territorial.
As for fish that dart being smaller - how else would they get away from predators in the wild? Unpredictable, rapid movement is realy crucial to their survival and they need to be extremely quick. Similarly, shoaling is an adaptation to avoid being the one that's eaten - if you're in a big group, it's more likely one of the other will be lunch than you

Of course, different species also have different ways of moving.
Why fish go in one direction and then suddenly stop mid-way is beyond me. This is where we border on educated guessing... They probably change their minds half way or see something more interesting elsewhere - short attention spans

Or maybe their like me when I go to the fridge to get something out and forget what it was I was after (oh come on people, you know something like that's happened to you too!). Perhaps they judge something as a threat and choose to turn away or feel a vibration/current you can't see and choose to move away/into it. Don't forget some fish have territories they stick to or that some 'follow' their reflections (particularly territorial fish). I've had several male swordtails that think pictures of female swordtails outside their tank are real and follow them around(random experiment a while ago...) so it's very likely they also react to movement outside, changes in light etc...
I have to say my fish tend to gather near the front when I'm near and then they start minding their own buseiness lurking between ornaments/plants if they can't see me. Cories tend to systematicaly search the bottom - except when they're spawning (which happens very often) when you see them darting up and down the glass franticaly, circling, turning upside down etc in an attempt to secure the eggs to plants/rocks/the glass... The fish like danios seem to forever be swimming against the current. As soon as they reach the source, they let the current sweep them back and start all over again

My black phantoms always move relative to each other. Tilting to show off their fins but always keeping a certain distance from each other. My pearl gouramies are usualy either socialising in a particular calm corner of the tank or searching everywhere for food. Occasionaly, being labyrinth fish, they dart to the surface for a breath of air. Obviously, I have various other fish and each behaves differently but I don't have THAT much time on my hands...
So, yeah, my 2 cents
