While going over bumps/potholes at slow/moderate speeds the car makes clunking noises from the direction of the wheels (front and back, not occurring at the exact same time.) Is this the sway bar bushings needing replacement?

The noise does not bother me and the car handles great regardless of a loose something-under-there, can I safely ignore this or will some problem exacerbate if I do not fix?

The only way to proceed is with a careful examination of all the suspension components, and replacement of all the ones that are worn. I cannot tell you what has failed, and neither can anyone else, without examining it.

"can I safely ignore this or will some problem exacerbate if I do not fix?"

I think you already know the answer to that question.

Well, are there any other suspension components that can make a clunking over slow bumps?

Yes, just about all of them, I'm afraid!

Since we are talking about suspension, what about about minor creaking when cold/cold weather over speed bumps, hard braking when reversing?

Does this tend to mean it needs new shocks, or are there some common spots that need some lube?

My clunking was attributed to the sway bar end links

I hope your fix is as easy as mine was

Why would you ever need to brake hard while reversing?

On the front for creaking....
Control arm bushings, upper and lower, they dry, wear and tear
Ball joints, upper and lower, they are nongreasable
Wheel bearings, nongreasable and wear to breakage, mine had a broken race
Frame connector bushings, another dry, wear and tear, but somewhat unlikely
On the rear....
The 'A' frame truss, especially if you used jack stands on it support the car while previously working on it. The sound will appear to be coming into your back seat.
For the clunking...
Front/rear shocks....fronts, check the towers and under the mounting post, the bushings are notorious for wearing out, you'll see lotsa orange bushing material. For the rear, the dampers wear out (similar to the tower bushings), but they are a big seat for the rears. This will sound like someone thumping from your trunk each time you go over a bump/pot hole.

Now depending on your vehicle...with or w/o CATS will determine what you need. If yours is without CATS, I may have a deal for rear shocks for you I bought incorrectly for my 2000 if you do those.
....all these will cause creaking from weight transfer and frame roll from being worn, dry rotted or plain broke. When you can hear it in the cab of the car, then its usually getting bad because of the solitude of a Jag interior.
The simplest solution is to go to most any tire/general fix it shop and ask them do a check of your suspension for a reason for the noise. It should take them about 45 minutes to an hour to run around and do the pry bar test. You can do it yourself if you have experience, but I figured you may not since your asking here.
If you feel so inclined to do so yourself, you'll need a large screw driver looking pry bar, about 30" long for leverage. I believe they have them at Harbor Freight at a reasonable price. You'll need a 2 ton floor jack and preferably jack stands, again Harbor Freight works. Put the front of the car on the stands on the factory jacking points behind the front wheels (should have plastic caps in them). Then take your pry bar and put it under the bottom center of the wheel and pick up...listen for your creak on both sides. If its only one side, remove that wheel, you will see the control arms, shock and sway bar end. Pry up on the suspension mounting points, ....you can also use the jack to pick up under the wheel studs a few inches using a block of wood (2x4 for example) in between to prevent marring the threads. Be sure to release the jack somewhat quickly to listen for your issue. You can do it from under the disc brake, but your dust shield may be in the way? Just be sure to use the wood to prevent disc damage.
If they charge you, it would be quicker and cleaner to have the shop do it and save you a lot of time. But most do inspections for free just to try to get your business and it would cost about the same for the jacks, jack and pry bar.

I think I covered most of the easy stuff?

Wow - this is great info. I will start to investigate this with this info, with the easy stuff first.

highhorse, I was wondering if you could explain which bit is the A frame truss, and what fails on it? Does it have bushings?

Yes, there are protective mounting bushing from where the truss mounts to the body. The truss 'A' frame leads back to support your rear suspension/drive line. If you replace your rear shocks, this assembly will have to come down to access that area. The bushing that will sound like its coming through the back seat is just in front of the rear wheel, about 6" in and you should see a 4" diameter rubber bushing with a big bolt through it connecting to the body. As you look back you'll see the 'A' frame leading to your rear suspension/drive line and over to the other side of the car.

Thanks for the explanation.

I found a diagram here :

REAR SUSPENSION for 2002 Jaguar XJR

So the truss is item 7, and the bushes are item 10, I think.

You got it....

90% of the time the "clunk" is cured by replacing the sway bar bushings and links, front and rear. Cost is less than $200 in parts IIRC and an easy DIY, although the front sway bar is much larger than the rear and tougher to muscle back in place by yourself.

Replace your front upper shock bushings too, about $70: https://www.jaguarforums.com/forum/x...cs-how-128562/
Vector

I had the same clunk and also had a nice vibration at 50mph to go along with it, replacing the steering rack and tie rods solved all of it.

Cheap and easy, drives like new.

Thanks vector, the 90% likelihood was what I was seeking as a starting point :-)

High horse, what am I looking for to identify worn shock tower bushings? Shrunken orange bumpers?

Vdp, if you do the work yourself, you will need nothing more than a floor Jack and jackstands. All the parts will cost under $200 combined. I bought the swaybar bushings from motorcar Limited, but lots of suppliers have them; bought the Moog links off Amazon; parts geek has the upper shock mounts for $76 each plus shipping (Rock Auto had them, cheaper, but now all gone). There are plenty of tutorials on this forum and on YouTube. See vectors thread. The upper shock bushings will begin to powder when they are badly worn.

The rear noise might also be the rear exhaust hangers; mine get noisy in the Winter; silicon sprays quiets them, but dried upper shock bushings are more likely.

+1 on Jhartz reply

I have the exact same situation with my front suspension it's only over smooth bumps never from a hard hit or anything. I guess I'll add that to today's list!

Rockauto has the upper shock mounts back in stock, I just picked up both right and left upper shocks mounts for $116 shipped.