Comment: A Lot Like Napoleonic Naval Combat (Score 1) 805
The first thing to do is constrain the question. "What would naval combat look like" would have a very different answer in 500BC than it does today. So let's assume that you mean, in the next few years.
The battlefield has the characteristics that movement is free, but acceleration is generally not; there is a complex set of small accelerations constantly acting on the combatants, and those forces are constantly varying with time; the environmental accelerations get substantially larger as the combatant's proximity to a large body increases, and also substantially larger as the combatant enters any atmosphere (and the closer in, the denser the atmosphere so the larger the acceleration); vision is essentially unimpeded except in the vicinity of relatively large bits of debris (somewhat larger than the combatant vessels); detection is simple because all manned or powered objects will radiate heat, and that cannot be particularly well masked within the laws of thermodynamics and both human and machine endurance. In the near future, we will not have the ability to accelerate for long periods of time or at high rates, except downwards (towards a reasonably close planet or star), because chemical and nuclear rockets have to carry fuel, and other known methods of propulsion (such as solar sails or electric propulsion like ion engines) generate low levels of thrust.
These characteristics favor a few combat methods. Long-range rockets, probably with warheads of some combination of boulders (resistant to weapons trying to destroy them) and pebbles (also resistant to being destroyed, and capable of doing damage over a broader area, but potentially could be armored against), would be the major weapons systems. Most likely, these would involve a short, fast boost followed by a long coast with the booster discarded, followed by last-minute maneuvering to hit the target - all of these characteristics intended to make the weapon less visible, and thus the reaction too late. There are some circumstances where rail guns or even low-recoil gatling-type cannon might be handy, such as in close-in combat around asteroids/planetary rings.
Because ships can be detected a long way off, but maneuver takes a lot of time (because acceleration costs heavily), it's likely that most of the combat will be very slow by modern standards. It might take days for two ships to fight a battle, with long range shots starting the action, followed by closing slowly once the long range ammo was gone, followed by either boarding (think like the boarding pods on B5 that attached to the hull and then burned through) or the aforementioned rail guns or other kinds of small, fast ballistic projectiles. Mines would be immensely popular, because they use almost no power and thus generate almost no heat. If they only transmit, and do not receive, their radio signature would also be quite small, so they would be very difficult to detect, but could still be command as well as proximity detonated. They would probably be nuclear, because that would increase the destructive radius substantially (especially from radiation and EMP effects; blast would be a minor issue unless the mine was right on top of a combatant, because there's no fluid medium to transmit the pressure).
So basically, in the near future, it would likely look a lot like Napoleonic naval combat.