oh yeah, its an 04 750, advanced with a TBR pipe.

The stock suspension consists of basically two parts at each suspension point (i.e at each fork and at the rear shock). The two parts are:

(A) a spring. The job of the spring is to push the wheel down against the ground faster than it would fall by gravity alone when it encounters a bump and wants to rise away from the ground.

(B) an oil damper arrangement of some sort (basically imagine motor oil and a plate with holes tied to the spring). It's purpose is to stop the oscillations of the spring to keep it from bonging repeatedly when the spring compresses and releases, by forcing oil through the holes as the main component compresses/releases with the extension/compression of the spring.

There is also a critical component that most people ignore and that's the tires themselves, which play a major role, in part because good tires can suck up minor bumps without involving the rest of the suspension system (the taller the sidewall, the better it will suck up road irregularities, but also the more likely the tire is to deform when the bike is leaned over, hence again a compromise). The tires should always be the first suspension component to be upgraded.

(And for the hyper-technical, there are other suspension components, such as frame flex, but we're going to ignore those because we're not talking about the level of alterations involving re-welding frames).
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The stiffer the spring, the faster the wheel returns to the ground (and the faster the tire makes good contact again), which is good for handling, braking, acceleration. The stiffer the spring, the less it will want to compact under load from above as well (such as braking dive at the forks, or sagging at the back for a heavy load).
But the flip side to that is that it won't suck up bumps as well for you (more of the bump will be transmitted to the rider rather than being squashed at the shock and/or forks).

The thicker the oil, or the smaller the oil valve opening(s), the more force will be required to get the spring moving and the faster the spring will want to stop cycling (boing'ing) because of the extra drag.

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Spring preload pre-compresses the shock some to increase it's effective stiffness. Bikes with superior suspensions have this option on both ends; the stock Kat only has it at the rear shock (the forks have no method for changing the spring preload). You can improve the fork spring by either replacing them with stronger ones, or by compressing them using a physical object to load them in advance (there's a $1 fork mod thread around here somewhere, where Black_peter explains how to use a piece of PVC to preload the fork springs).

The damper adjustment on the forks & shock move a cone-shaped needle into the main hole the oil passes through; the closer the needle is to blocking up the hole, the harder it is for the oil to flow, increasing the damping rate, thus changing how fast it clamps down on the oscillations, but also how much force is required to start the spring moving.

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Common issues/complaints:
Any time you take oil and force it through a small opening repeatedly, it breaks down (loses it's viscosity, some of the molecules get ripped into smaller pieces, called mechanical shear). Additionally, as it is forced back and forth, the oil heats up (resulting in a tiny bit of thermal breakdown), plus the metal the holes it passes thru expand as the metal heats up from the heat in the oil (changing the size of the holes).
As a result, the maintenance schedule calls for replacing the front fork oil every two years (along with the seals). Unfortunately, far too many riders let this bit of maintenance slip away for quite a number of years past it's due date.
The oil in the rear shock breaks down too, but the OEM shock has no way of replacing it (no place to open & change & reseal the shock, unlike high-end units from Ohlins, etc).
The other complaint is that the springs are too weak. Sometimes it's from them being overtaxed and aging (or simply because the factory really does use weaker springs than a typical American's weight would dictate), but more commonly in my experience, its actually the rider's skill level improving enough to notice that the stock springs ship too weak OR the rider's body weight increasing with age and noticing the change in the bike's behavior OR the decrease in the performance of the oil playing into the shock's behavior in general.

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Top-of-the-line suspension equipment uses either tricky bits to control the oil. Some use a combination of one-way oil-movement valves (how they can separate the motion clamping) or sprung flaps on the openings (so different amounts of force open different numbers of passages). The Ohlins I had been selling as clearance items use a series of flat plates attached to a remote adjuster -- changing the setting tightens up the space between the plates, reducing the flow rate. Additionally, it has an aluminum needle valve system which is designed to grow at exactly the same rate as the oil thins from heat, so the passage sizes at the bottom remain the same.

The springs themselves are nothing special, just some specific strength wind, usually a bit stiffer than the OEM springs. Some springs use progressive spring rates (the windings get tighter from one end to the other), so it takes less force to compress the first little bit than the next little bit, etc (the stock springs are said to be progressive rate springs). There are also dual-rate and tri-rate springs on the market (although I've never seen any specifically for the kats), where each section compresses at a different rate.

The problem with buying used, is that unless the used shock is either rebuildable by design (most Suzuki OEM shocks aren't), or is fairly new (say off a wrecked two year old bike), it's likely to be just as toasted as the shock you already have...

Hope that provides some clarity.

Cheers,
=-= The CyberPoet

There's a shock swap sticky you might wanna look at , too ...

That pretty much sums me up.

2001 Kat purchased in 2002, now with 45,000+ miles on it and I still haven't changed the fork oil.

I have been looking into Works Performance shocks and springs, though.