Clunking noise from back end bmw x3

SOURCE: CLUNK IN REAR

There's a few more things to check out:
1. The track bar links, which attach from frame to the sway bar. Inspect the bolts/nuts to ensure they are really tight and the rubber isn't worn to the point of slack.
2. The bushings where the upper control arm attach to the frame. Inspect these for torn rubber/missing bolts. (These 2 bushings are on the fore end of the wishbone where you changed the upper ball joint.)
3. The bushings in the other, straight control arms that restrain the differential.
4. The shock absorber bolts/rubbers at frame and axle.
5. The u-joints on drive shaft.
6. The differential input pinion bearings. Raise vehicle and really yank/pry/push around the drive shaft and look for any slack.
7. The drive shaft at transmission. Check for any play over 0.020", side to side, up and down.
8. The transmission rubber mount.
9. The axle bearings. To check these, lift under axle, each wheel, and yank wheel fore/aft, up/down, and maybe use a pry bar. You're looking for axle bearing wear where the axle is supported at the outer ends of the axle tubes, just behind the brake mountings.
10. While the vehicle is raised (wheels off ground), chock the front wheels, and put transmission in neutral. Now check for significant slack when you manually rotate the wheels by hand, back and forth. If slack here (say, 10-15 degrees of fore/aft rotation on a wheel), then the spider gears are probably worn at the cross shaft in the differential carrier. Depending on the amount of slack, you can change the spider gears, side gears, cross shaft, and the associated thrust washers yourself, if you're a capable mechanic. This requires opening the differential cover, removing the rear axles (at least far enough to get the axles out from the side gears), remove the cross pin retainer bolt, manipulate the cross shaft out, manipulate the spider gears with their thrust washers, out, manipulate the side gears, with their thrust washers, out, then replace the above, with a 'gear kit', which includes the side gears, new thrust washer, spider gears, with new thrust washers, cross pin, and cross pin retainer. A 'gear kit' is around $85 for the Dana 44, 30-spline axle kit. While those parts are out, pry the carrier in each direction inspecting for slack in the carrier bearings and check the pinion/ring gear slack at that time. If you find a bad carrier bearing or pinion bearing, then you should probably find a mechanic to replace those, unless you're a 'very capable' mechanic. After reassembling the gear kit (side gears with their respective thrust washers, spider gears, with their respective thrust washers), cross pin, and retainer bolt, clean the sealing mating surface of both the axle housing and cover, remove the fill plug from the cover, apply RTV sealer to the cover (1/4" bead), attach the cover with bolts, replacing the tags in their original locations, refill differential with either 85w oil or 70W140 synthetic, as desired, approx 2.3 liters, replace plug, and check for leaks. Note: when removing the differential cover, remove all but 2 mid-side bolts, and make them loose. Then tap the very bottom of the lid towards the rear to loosen the cover, have drain pan under the differential to catch the oil. Then remove the 2 remaining bolts and cover. The lid projects below the housing about 1/16" and that is the part of the lid you want to bump on to loosen the cover.
11. Rear disc brake caliper mounting brackets.
12. The sway bar rubber mountings on the axle.

.. and that pretty much covers everything that can make noise on/in the rear end.

13. If a tow hitch is attached, check that for proper attachment.
14.Fuel tank loose, or fuel pump inside tank loose.
15. Spare tire loose, or junk in the spare tire carrier hole.
16. Loose junk in the right rear side compartment (this is actually a CD changer compartment, but if no CD changer is installed, then people put all kinds of junk in there)
17. Rear lift door. Open it a bit and check for side to side play. I've heard of terrible noise on my rear lift gate, and it was the rubber wind seal making a bunch of noise. I wiped it with a rag I sprayed silicone oil onto and quieted that down.

SOURCE: when turning steering wheel - either way, clunking sound.

Sounds like you have a bad CV joint, this will make a clunking or clicking noise like you described only when turning, and varies with vehicle speed.

Have it repaired before it breaks and leaves you stranded, or damages anything else.

SOURCE: clunking popping noise from rear end when tires

the gears in your rear end are probably chipped and broke or need shims

SOURCE: Loud Clunking when jeep starts moving in drive.

may be the gears in the rear end or check your motor mounts, ive had the noise and it was motor mounts

SOURCE: 2005 equinox devolped a clunking

Not likely more common for sway bar links. The upper and lower portion of the links become loose and cause a clunking noise turning or over bumps. They are also known for the lower intermediate steering shaft. This is more common and noticeable just turning especially in parking lot maneuvers (not going over bumps).