The simple answer is they wouldn't, unless entirely new technologies and science come to support it.
The style of combat you see in these movies is based on air-to-air combat. The key to this is a physical reality of flight: in airborne flight, you can always trade forward velocity for acceleration. You do this by turning your vehicle and letting the aerodynamics accelerate you to one side or the other at the expense of drag.
In real space combat, such accelerations are exorbitantly expensive. You don't have the atmosphere to push against so you have to supply your own reaction mass. The ISS has enough fuel for about 50m/s of delta-V (source, doubled because they were concerned with fuel from a resupply, and the ISS has about 2 resupplys worth of fuel onboard). That means they can change their velocity 50m/s, or 110mph. Given the orbital velocities on the order of 8000m/s, you can see how that change is very small.
Very small indeed. We can calculate that in terms of air forces if we were in the air. Air-to-air combat people often phrase these energy budgets in terms of G-seconds. 1 G-s is the energy you bleed off making a 1G turn for 1 second. We can see that 50m/s is roughly 5 G-s. Now we need to calculate how efficiently we turn. The Lift over Drag(L/D) of a fighter varies based on how hard it is turning, but 5 isn't unreasonable, and you could even argue for 10. This means that if we do a 5G turn for 1 second (50m/s^2), we will suffer a drag force decellerating us by 1/5th of that: 10m/s^2.
This drops our velocity by 10m/s. If we were traveling at 300m/s (subsonic), we'd end the turn at 290m/s.
To pull this together: A fighter plane without using their engine can pull a 5G-s turn bleeding a mere 3% of their velocity, and the resulting turn is roughly the same as the complete maximum divert budget of the ISS. It won't take long for the fighter's engines to recover that velocity.
This means that, in general, trajectories in space combat environments are much more predictable than they are in air-to-air combat. Obviously your space fighters will have a much larger divert budget, but they are limited by the maximum efficiency of the fuel. A medium sized maneuver for a F-15 in the air might consume the entire delta-V budget for a mission in space.
It is this predictive nature which changes the way you fight in space. Just as you shoot at the enemy from afar with a gun rather than going in with a knife, there's basically no reason to get to the distances we see in fiction movies, nor is there a reason to let the enemy get to those distances. You kill them long before that, because they're so predictable.
Accordingly, space combat is fought at a much more strategic level, with long distances between objects making it harder to be killed. That shapes the real fight.
In order to get the science fiction image of a dog-fight, you would need a completely revolutionary propulsion system. A key number for this is Specific Impulse or (ISP), which is a measure of how much delta-V you get from each unit of fuel you have on board. I like to think of it in N-s/kg (which measures impulse per unit mass), but many people use the units of s (that's seconds), because that's the units you get if you measure impulse per unit weight. (Generally I find Americans prefer ISP in seconds because the English unit for impulse per mass is pounds-seconds/slug, which is just a horrible unit). I'll report seconds here, because its easier to find data in those units.
In any case, our ISPs are very limited. Chemical rockets, like we use today, can get into the 250s range, and ultra-fancy hydrogen-oxygen rockets get to 450. Nuclear pulse rockets (which lob nuclear bombs out behind them for propulsion) can get to 6000s reasonably, with a theoretical maximum of 100,000s. That's only 400 times greater than the ISP we have today, so even with the theoretical efficiency of nuclear pulse rockets, you're still barely approaching the capability of a fighter plane which gets to run its engines for a few minutes.
So what you'd need is a completely new approach to physics which permits unattainable levels of maneuverability.
One approach might be to break non-locality. If you had a way to impart momentum into the air of a nearby planets non-locally, you could use that to achieve air-to-air style maneuverability. This might also lead to some fascinating combat techniques where one identifies the volume of air that you are maneuvering with, and actively messes with it to disrupt your trajectory (like yanking the seat out from underneath someone before they sit down).