Ship-vs-ship
-Next Generation era
In The Next Generation episode "The Wounded" USS phoenix destroys Cardassian warship from distance of around 200 000 kilometers with display showing Phoenix' weapons range to be 225 000 km and weapons range of Cardassian warship little less than 270 000 km). Phoenix destroyed Cardassian warship with torpedoes. Later, it destroyed supply ship from range of about 170 000 km, presumably with phasers.
In "A Matter of Honor" Riker advises Klingon captain attempting to attack Enterprise-D to close to 40 000 kilometers before decloaking in order to shorten their response time (he needed BoP in transporter range for his own purposes).
In DS9 "A Call to Arms" we seem to have 10 km range for Dominion/Cardassian weapons, but that is not actually true - VFX Supervisor David Stipes (who should be fired if his work is always like that) added station in order not to confuse audience where fleet is actually going. So that example can be dismissed. Especially considering that in "The Search" we have >100 000 km weapons range for Dominion "bug".
In any case, given that short-range battles usually occur against enemies with similar fighting capabilities, it is unlikely that Federation or any other Trek power would not use it if it could help.
However, there are some reasons for shorter-range fights (in-universe reasons, not RL reason that it looks "pretty"). Shorter range also shortens enemy's response time, and makes it harder to evade beams. In "Sacrifice of Angels" and both battles of Chin'toka, we have one fleet trying to push throught other one.
Conclusion: Effective weapons range of Nebula class starship is 225 000 kilometers for torpedoes and 170 000 kilometers for phasers.
-TOS era
In TOS, long combat ranges are relatively standard when compared to TNG era. In episode "Changeling" we have probe firing on Enterprise from 90 000 km, which is "at end of their sensor range". Enterprise returns fire by using photon torpedoes, from same range. Probe is 1 meter high and 0.25 m wide (as seen after teleporting to Enterprise).
"The Ultimate Computer" shows weapons range of around 200 000 km (it also informs us that penalty for mass murder - or murder - is death - M5 attempted to committ suicide after learning that it caused death of 400 people).
Orbital bombardment
In "Skin of Evil" Enterprise-D destroys shuttlecraft lying on surface of planet from range of around 0.8 to 1 planetary diameter, or 10 to 13 thousand kilometers. Given that they were targeting small shuttlecraft, and that Nebula-class USS Phoenix demonstrated 200 000 km effective range against 400-meter long Galor-class warship, ranges of around 1 000 000 km for carpet-style planetary bombardment are possible.
Star Wars
Ship vs ship
In Return of the Jedi, we have engagement ranges of around 40 kilometers in beginning (200 km as high-end gross overestimation); later, Rebel fleet closes to "point-blank" range - Rebel cruisers basically enter into space between Imperial Star Destroyers, reducing engagement distance to few hundred, and, in some cases, few tens of meters.
Orbital bombardment
Hoth ion canon was able to hit Imperial Star Destroyer from distance which looked like 0.8 to 1 planetary diameter; assuming Hoth as Earth-sized planet (which is reasonable assumption, given that gravity on Hoth seemed to be normal), that gives us range of planetary defences versus 1.6 kilometer long capital ship as 10 to 13 thousand kilometers.
From that we can assume 4 to 6 thousand kilometer ranges for ship-vs-ship combat. (Speed of TL bolts seems to be few kilometers per second to few tens kilometers per second - that means that few hundred to few thousand km ranges are maximum against ISD-sized capital ships from SW).
UPDATE: In Revenge of Sith we have classical Napoleon-era naval tactics, with ships firing broadsides from point-blank range, as seen here:
That, however, is not point - point is that these guns have extremely limited arc of fire, 30 degrees on each side (assuming guns can change horizontal orientation; we saw no proof for that and, indeed, no visible mechanism that would indicate such ability. However, it seems that guns could elevate barrels vertically; possible elevation seems to be from +30 to -30 degrees.
For comparation, main guns of WW2-era Japanese Kongo class battlecruisers and Nagato class battleships had maximum elevation of +43° for main guns (negative elevation was not so important due to most battles being fought at long range - few night battles occured at short range before advent of shiboard radars and in such situations ships could find themselves in awkward position of not being able to lower their main guns low enough to actually target enemy ships. Same issue was with sinking of Prince of Wales and Repulse - British gunners were unable to achieve low enough elevation (actually negative elevation was needed) to target Japanese planes).
Darkstar here says that guns cannot elevate barrel nor turn left or right. While he is right about guns being unable to target ships that were either left or right from direction barrel is facing, his argument about guns being unable to elevate barell is flawed... Gun does seem to have mechanism to elevate barell, but barell would have to be at zero elevation to be reloaded, similar to WW2 era guns, picture seen below.
However, shell storage mechanism is wierd; but again, it could be that gun had some system that only allowed one shell to fall into loading mechanism.
UPDATE: Speed of TL bolts might be 5-10k meters per second at most. Given manouverability and speed of capital ships, actual ranges are closer to 100-500 kilometers.
UPDATE 2: It is suggested on Wong's site that TL bolts have physical projectile at their core. If that is case, then green "bolt" might just be "tracer" or "marker" to allow gunner to determine if bolt actually hit its target. Speeds of modern artillery shells reach up to 1600 m/s as per this page; given that there is no air resistence, speed of bolts as seen in movies might be possible. However, that can't explain TESB asteroid vaporization scene.
UPDATE 3: I just remembered that in ANH (both novelization and movie) Wedge Antilles commented during Rebel briefing that "not even computer could hit it" (2 m wide exhaust that was discovered to be weakness). That seems to suggest even lower effective ranges than previously calculated (at least for torpedoes).
UPDATE 4:
RotJ novelization:
"ADMIRAL Ackbar stood on the bridge in stunned disbelief, looking out the observation window at the place where, a moment before, the Rebel Star Cruiser Liberty had just been engaged in a furious long-range battle. Now, there was nothing. Only empty space, powdered with a fine dust that sparkled in the light of more distant explosions. Ackbar stared in silence."
This could mean, combined with evidence from movie itself, that maximum effective range for capital-ship battle is less than 500 km.
UPDATE 2: It seems I was wrong - mechanism I thought was for elevating barrell is actually recoil mechanism.
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