I'm assuming this could cause Death Wobble?
 

I bought my '95 ZJ for $350 from a co-worker and after new shocks, radiator, plugs, battery she was on the road. It's always had DW, but I know how complicated it can be so I've been putting it off. I have to replace the transfer case so I figured I'd start digging into the front end as well. Got under the Jeep and I saw this! Passenger side swaybar link snapped off.

http://home.comcast.net/~tgfmo/link1.jpg

Driver's side not so pretty either

http://home.comcast.net/~tgfmo/link2.jpg

I'm thinking it's a good place to start and will replace both sides while I'm at it.

The sway bar won't cause DW. Keep looking.

Rats, should have known better since guys take them off! Guess I'll start with a good alignment, move onto the trackbar, etc..

Worn track bar bushings, control arm bushings, steering linkage, ball joints, and unit bearings will contribute to DW. Notice I didn't mention the steering stabilizer?

Unless you check the trackbar and control arm bushings, an alignment is a waste of money.

True that. An alignment before repairs is like wiping your butt and then taking a dump.

Busted, You do have a way with words!

Also, point of fact. I drove me WJ for about a week with the steering stabilizer disconnected. I didn't even notice any change in the handling.

I tried a couple of tests on the trac-bar and it didn't appear to be loose, but it's nearly 20 years on the original parts so I figure almost all of it could use replacing.
I've read numerous times that the steering stabilizer is a band-aid at best and not the root of DW. Piece by piece I reckon...

I noticed from your pics that the undercarriage is quite rusty. Watch carefully the control arm mounting brackets on the frame. My 97 ZJ tore one out of the frame in the rear. After gusset welding about 75 lbs of steel into it, the fronts started cracking. Time to part it out.

Polyurethane track bar bushings help quite a bit with handling feel and DW. I installed poly bushings in both track bars on my ZJ, and changed all of the control arms. I plan on swapping the front lower arms to WJ arms very soon. Already have WJ upper arms, a change for the better.