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I think the key to Saturn's rings at least is accretion discs. I.e the material that makes up both the planet and its discs was a rotating mass before the planet formed.
Once rotating, the equator of a body has a larger circumference than one that passes through each of the poles. This then helps to keep the rings bound to the same plane as the equator.
Not sure about galaxies or solar systems though - however I suspect that similar forces are at play.
--
On a side note, while looking for an answer I discovered that one of Saturn's moons is emitting some 1000kg/s of water vapour from it's South pole, which is then ionized and rotates around Saturn. Neat stuff. Thanks http://en.wikipedia.org/wiki/Magnetosphere_of_Saturn[^]
"When I was 5 years old, my mother always told me that happiness was the key to life. When I went to school, they asked me what I wanted to be when I grew up. I wrote down 'happy'. They told me I didn't understand the assignment, and I told them they didn't understand life." - John Lennon
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enhzflep wrote: the equator of a body has a larger circumference than one that passes through each of the poles
That seems to me to require that body in question be an oblate spheroid.
«I'm asked why doesn't C# implement feature X all the time. The answer's always the same: because no one ever designed, specified, implemented, tested, documented, shipped that feature. All six of those things are necessary to make a feature happen. They all cost huge amounts of time, effort and money.» Eric Lippert, Microsoft, 2009
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Yup. Sorry for being imprecise. 
"When I was 5 years old, my mother always told me that happiness was the key to life. When I went to school, they asked me what I wanted to be when I grew up. I wrote down 'happy'. They told me I didn't understand the assignment, and I told them they didn't understand life." - John Lennon
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I've thought about this before and my theory is:
1. Varying strengths of gravitational forces depending upon the plane in which something is orbiting is in (so everything over time settles into the gravitational plane where the strength is greatest), combined with..
2. Everything that wasn't in that plane has at some point collided with another object and either merged with it, adopted the same orbit (according to rule 1) or been knocked out of orbit.
That's just my guess though, if anyone knows better it'd be interesting to hear 
How do you know so much about swallows? Well, you have to know these things when you're a king, you know.
modified 31-Aug-21 21:01pm.
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it´s a feature of rotating bodies.
it makes sense really, something in the ecliptical plane has sufficient speed (and thus force => centrifugal force) to counteract the force of gravity. The more above or below the ecliptical plane you are the less counterforce you have for the gravity and thus you fall into damnation (or into the planet). The rotation is caused similar to putting satellites into orbit. They still fall, but the speed is sufficiently large to miss the ground. And let that just be the knack of flying  .
So basically it starts out as a "sphere" of debris, but only the debris in the ecliptical plane survives .
Hope this makes sense
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The angular momentum wasn't evenly distributed, and one specific direction "won". The rest cancelled out by collision.
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This is the correct answer. And the same answer applies to all systems: why most of the mass of our solar system orbits near the ecliptic; why Saturn's rings are flat; why galaxies are flat; why most moons orbit in the same direction and plane as their planet's equator; etc.
That which has not yet "canceled out by collision" remains spherically distributed, i.e., the Oort cloud on the outer reaches of our solar system.
And, of course, there were local maxima and minima in the original distribution of angular momentum, which could explain, for example, retrograde orbits and why Uranus and its largest moon Triton rotate and revolve in a different plane from most of the rest of the solar system.
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Organizing Principle?
There probably *were* other bodies going in various orbits at one time...they all collided, over and over, sometimes breaking up into smaller pieces which tended to follow the majority of bigger pieces (sometimes absorbing them due to higher gravity) that travelled in the same direction and on the same plane...eventually all that is left are things that occupy their own safe orbit on the same plane.
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I *think* the narrator of that *may* be lacking his meds; or have taken too much.
veni bibi saltavi
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That looks like just the ticket! Unfortunately I need to wait until I get home to click the link. Doing so is not in the interests of my employer. 
Regards,
Rob Philpott.
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That's a very cute explanation of particle collapses.
Shame it's not believed to be relevant to our solar system.
Lookit: if one of the big lumps of our solar system were to decide to go off in a non-planar orbit (as they have many times in the past, through collisions, etc.), the gravity of all the other, lumps whizzing past them would slowly pull them back into the plane, and also "correct" their velocities.
To avoid that, they would need something to give them a drastic change in velocity.
So, the rule is: If you want to jump out of the plane, take a parachute.
I wanna be a eunuchs developer! Pass me a bread knife!
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Space Weevils.
They nest in rocks, and obviously grouped them together to make building nests easier...
[In reality it's Conservation of Momentum: when gravity collapsed the original cloud the solar system was formed from, this caused the trivial spin it started with (the average "movement" of all molecules was in one direction or the other, a "zero-average" momentum is a very unlikely case) to increase in the same way that a ballerina pulling her arms inward spins faster.
Once the mass is spinning "properly" a disk forms as it's the least-energy configuration.
Same thing happens with planets and moons on a smaller scale.]
But I prefer the Space Weevils.
Bad command or file name. Bad, bad command! Sit! Stay! Staaaay...
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OriginalGriff wrote: But I prefer the Space Weevils Sheep.
ftfy
veni bibi saltavi
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Sheep?
Sheep don't make nests!
Bad command or file name. Bad, bad command! Sit! Stay! Staaaay...
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The universe if flat and if you go too far you fall off.
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That's going too far.
Toodles!
I wanna be a eunuchs developer! Pass me a bread knife!
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It's like gravity, Man.
The big lumps are trying to fly away from the Sun, but they're also pulling each other together, so the only way they can go is to align on a plane.
I wanna be a eunuchs developer! Pass me a bread knife!
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The answer is simple. Me and Chuck Norris agreed it should be this way.
".45 ACP - because shooting twice is just silly" - JSOP, 2010
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You can never have too much ammo - unless you're swimming, or on fire. - JSOP, 2010
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When you pry the gun from my cold dead hands, be careful - the barrel will be very hot. - JSOP, 2013
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He's the guy who rick-rolled Rick Astly.
He's the guy who can strangle you with a cordless phone.
He's the guy who invented lowercase letters - to show the capital letters who's boss.
Bad command or file name. Bad, bad command! Sit! Stay! Staaaay...
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Yeah I've just googled Sounds like a raging Homosexual.
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How do you google "sounds" like a raging homosexual? By delicately typing with a lisp?
".45 ACP - because shooting twice is just silly" - JSOP, 2010
-----
You can never have too much ammo - unless you're swimming, or on fire. - JSOP, 2010
-----
When you pry the gun from my cold dead hands, be careful - the barrel will be very hot. - JSOP, 2013
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It looks like you're failing to undrestand the gravity of the situation.
I always wear my coat, guess why?
Geek code v 3.12
GCS d--- s-/++ a- C++++ U+++ P- L- E-- W++ N++ o+ K- w+++ O? M-- V? PS+ PE- Y+ PGP t++ 5? X R++ tv-- b+ DI+++ D++ G e++>+++ h--- r++>+++ y+++*
Weapons extension: ma- k++ F+2 X
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