Let's get this one out the way: the following is the money shot when it comes to seeing the old Enterprise shoot at something:

Those bright blue beams of intense energy radiating towards the Klingon / Tholian / Orion / whatever - it's like seeing what lightsabers of unlimited length can do (without the cool sounds). Of course, from this viewing angle of the ship, these beams shooting in such a wide spread pattern makes one wonder if double pin-point accuracy is going to be achieved at space-faring distances. The enemy ship would have to be practically point blank range if both beams were to hit, unless it's the size of the First Federation vessel.

Heavy-duty ship phasers apparently evolved over time. Here's a rather pathetic-looking Starfleet variation used when engaging the Gorn:

I think the effects folks needed to move the phasers' point-of-origin a bit more. Sometimes the Enterprise fired into the atmosphere, like in "The Apple" and "Who Mourns For Adonais?"

Earlier in the first season in "The Corbomite Maneuver," we saw this:

The phasers sure look cool with a nice glow around it. The feeling of power is evident. You wouldn't want to be on the receiving end of this one. Take that you little spinning cube of death!

But these recycled shots of the Enterprise from this angle kind of gets old, doesn't it? So here's a shot from a different angle taken from "The Doomsday Machine" where phasers shoot so fast that you can't tell if they trail. They just simply "turn off" after they've left the emitter (which is apparently the bottom dome in this episode):

Let's get back to the original over-used Enterprise beauty angle. Ship phasers weren't always long streaks of blue / red / pick-your-color. In "Balance of Terror" they were shot bursts that suspiciously reminds one of photon torpedoes. But they're phasers. Make no mistake about it. The Captain said so.

Phasers wouldn't be phasers unless you could tune them, of course. Starfleet is always on a mission of peace, so naturally in "The Piece of the Action," we have to see the ship perform a planet-side stun setting in super-cheesy green.

The only thing missing from this picture are some cartoon captions that say "Pow!" and "Zap!"