This is quite obvious if, like me, you've played the Star Trek MMO where the game designers were inspired by the motion of the ships in the movies. I think it's most noticeable when the Bird of Prey in Star Trek III attacks the Enterprise.
Is there a canon explanation for why the ships in Star Trek bank when turning?
Please only give in canon answers, there are any number of debatable non-canon reasons, but that's not what I'm asking for.
I'm going to be bold and say that there isn't a canon explanation for the slight banking effect you see on screen. However I'd quite happy to be proved wrong because it would be nice to have a solid answer that fits what we see.
To backup my assertion and to assuage @DVK's concerns - I have seen every movie (several times), every episode of every TV series, played the same MMO the OP has, played a number of other Star Trek games, and read a selection of the books. I cannot recall, and I have a good memory, ever seeing any explanation for banking.
There are a number of scenes from TOS where the Enterprise does not bank in order to turn, so its usage is inconsistent throughout the TV series.
One theory I've heard, though it seems more conjecture than based in anything from the ST universe, indicated that banking the ship for a turn would decrease the power required by the inertial dampeners and artificial gravity in order to keep the crew unaffected by the turn. In other words, in a banked turn, much more of the inertial force is along the vertical axis, which would keep it in line with the gravity plating in the ship's decks, requiring less effort from inertial dampeners.
I would say it's simply an artifact of old thinking from the The Original Series. People know planes and banking was just something that is expected. Also it's hard to represent motion in space so banking helps represent that. The only in universe explanation I could think of is for tactical purposes. Since every race seems to have nimble maneuvering thrusters it would be a tactical disadvantage not to have them.
If we interpret "canon" as anything on-screen - imagery, dialog, etc. - then by that metric, no explanation is given. There is no dialog in any of the series about how ships maneuver beyond the occasional mention of thrusters. There are no effects shots showing thrusters or other mechanisms causing the vessel to bank as it turns. In fact, apart from a shot in TMP where they light up the impulse engine and the ship accelerates, there aren't any effects shots showing any relationship between engines and the ship's movement.
If we extend the definition of "canon" to include any production notes, writer's guides, etc., then...I don't know, I don't have access to any of those things. But if there is a canonical, in-universe explanation, that's where it would be.
I think you are all thinking of it wrong... there wont be a "canon" explanation... you need to think of it like bsg reimagined. when they did the original test shows they made the space fight scenes devoid of sound, and albeit realistic it did not go over well with the crowd. They expected to hear the guns and space craft.
so while thinking of that remember that the enterprise is a SHIP and people expect ships to bank and roll slightly when turning. Even boats do this, its called squat.
Well, let's give a bit an "inverse" explanation:
First, look at the design tables of most of the big star ships. Not the little shuttles, but ships like the Constitution or Galaxy-class.
These ships have only three ways of propulsion: Warp-drive, impulse-drive, navigational thrusters.
The warp drive is clear, it's a drive that only provides a forward acceleration, you can perhabs modulate the warp field a bit to make it a little bit left or right focussed, but it would make much fuss to configure it to go sidewards, especially during the flight itself. So they prefer, when they have to turn, to turn the ship with the navigational thrusters and so changing the direction of the warp field.
But the navs (I shorten it from here on) are much less effective than a warp drive. There are more like the rudders of ships and you can see it on designplans, are not on the front, side and back part of the ship, but in a 45 degree angle on the saucer plates. Even with the never more V-shapes ships. So, the only way to turn a ship in warp is to change the direction with the short nav on the right back of the saucer to make a left turn and vice versa. And this LOOKS like banking, but it's just a long turn, because the ships warp drive is much stronger than the navs.
But why also in normal space, when they are in orbit.. Well, the major drive there is the impulse drive, a fusion based drive with the power to accelerate the ship up to 0,92 c (on Intrepid classes). They never do this, full impulse is 0,25c, but just to avoid relativity effects to the crew.
These drives are also, like the warp drives, just forward drives, they cannot turn the ship. So you need the navs again. But the navs are also much less strong than the impulse drive (you can only go up to 1/4 impulse, as they explained it some times inverse, with only navs), so also here: when the ship is already moving with working impulse drives, they will always accelerate the ship to 0.25c, also in turns, and the navs can only adjust 1/4s of direction change in the movement. Yes, they could turn off the impulse drive, turn the ship with the navs faster and turn the impulse drive back on, but that would cost more energy and is more dangerous, as you would have to adjust all the initial dampers to the direction changes, and that twice. The ships are so big, that they don't need friction or ground to break themselves, they could do it by themselves, when the structural and initial dampers in the back of the ship are not adjusting in completely the same amount than the front part of the ship.
So, but what are the navs then? They are antigrav drives. Antigravitation must be known in that time, as they have artificial gravitation and can even build deck plans, that are completely against any common sense on modern space vehicles (for comparison, the babylon 5 station is, although not even moving, build so, that the decks of the station are from the front to the back, just because they have no artificial gravitation and need to rotate the living quarters to make g for the inhabitants, only the command section seems to have a weak artificial grav unit (perhabs bought from the centauri or minbari)). So, they use the antigravitation drives to navigate the ship, also to stop it (by cutting off the impulse drive and using the forward left and forward right navs to stop), but for more antigrav drives seems to be too weak.
Also this is physically plausible: Although antigrav drives would be super here on earth for easily leaving the planet, you cannot use them to get even near light speed, as you would need more and more energy to move your ship towards the light barrier (Einstein). So antigrav drives are just like in star trek only good for slow underlight flights (like shuttle, navigation rudders or keeping a space station on it's place), but not for interstellar travel.
So, why do they bank? Well, the nav thrusters are antigrav drives. And the most gravitational force is the ship itself, it's mass is high. So, to turn the ship while full warp or full impulse the most effective way, you gear the nav drive direction away from the ship, so, when you want to make a left turn, you start the right navs and gear them towards right down, and the left navs and gear them towards left up. So you use the mass of your own ship to turn :)
And yes, you have no clue by any dialog about the things I explained upwards, but it's only physical sense + design of the ships + seeing what they do.
But the most effective answer is of course: banking looks much cooler than like in "Interstellar" the direction changes :D
