As the title says, which lock do you use when cycle touring?  Do you even use one?   

The AXA Defender a dutch lock, you can see how it locks the back wheel. Permanently on the bike, key can't be removed unless locking the bike. Keeps from the spontaneous rolling away with the bike for quick stops. For longer times away from the bike, we use a thin strong cable lock to lock the bikes  together and to a stationary object. 

We've found this to be one of the best theft deterrents:

Somewhat seriously!

Having recently purchased a new bike, I've been wondering about this lately, and was considering posting the same question. I spent some time doing research and made a spreadsheet with the name, weight, who recommended it, the rating, the cost, and the interior dimensions.  I googled "best  bicycle locks" and ended up looking at more than fifteen lists, and found that most of them had the same top locks. Of course, I realize that the website raters get a kickback if you click on their link and buy that lock, so it might just mean that they're the ones who got their products out to the people who rate locks. Even so, it's at least something to go by. 

The other consideration is where you'll be using it. For some people, weight doesn't matter. If you live in New York City then you'll need a super heavy duty  (and therefore heavy) lock. On a bike tour in rural America? Small town Europe? I don't know.  Maybe dental floss would be satisfactory. I remember reading something before my first bike tour in 1982 that stuck with me:  the best lock is your eyes.

Kryptonite Evolution Mini-7 Bike U-Lock with Cable
3.55 lbs
USD66.00
7 inches (plus cable)

Kryptonite New York Fahgettaboutit Mini Bike U-Lock
4.55 lbs
USD 120.00
6 inches

Hiplock D1000
4.3 lbs
USD300.00
20 inches

Litelok X1
3.7 lbs
GBP150.00
7.7 inches
(8 oz heavier than 2 Apex Ti)

Altor Apex folding lock
2.4 lbs
USD98.00
30 inches

Kryptonite New-U New York Lock
4.45 lbs
USD111.00
4 inches x 8 inches

Abus Granit X-Plus 9"
3 lbs 12 oz
USD95.00
9 inches

Kryptonite cable
1 lb
USD17.00
4 feet

I ended up buying the Altor Apex folding lock. I haven't had it long so maybe I need longer to get used to it, but I find that the folding aspect makes it awkward. Additionally, you lock it by pushing a button, which is in a location where you handle the lock; therefore, it gets accidentally locked frequently. And, even though it's lighter than many, it is not light. So far, I'm not sure I'd buy it again. I miss my old cable lock, but from what I read, they aren't very secure... but then, back to my previous statement:  what kind of lock do you need in rural America?

The other responders have covered most of the areas. If they want you bike badly enough very little is going to stop them, particularly with battery powered angle grinders readily available. Rohloff owners may be interested to know that there have been instances in London England where the hubs have been cut out of the spokes for easier escapes with the hub hidden from view in a bag!

ATM ebikes seem more popular to thieves due to their popularity.

I carry a light cable lock and try to leave my bike among more expensive ones

A (little) more serious answer to your question:

We use ABUS locks, one Granit U lock and one Bordo folding lock. We also have a ~1 m long vinyl coated cable as well but rarely have to use it. We’ve found ABUS to be better quality (re key and lock mechanism) than Kryptonite.

Like RacPat do, we lock our bikes together (and leave the laundry drying on them!). Our bikes are also equipped with PitLocks on the wheels, seat posts, lights and brakes (a bit overkill but then you can just put a lock around any part of the bike that is convenient).

As Mark mentioned, the best lock ‘are your eyes’, or to take it further, other peoples eyes. We tend to park our bikes in higher traffic areas in plain sight. The biggest risk is at night and they are either beside our tent (on the now rare occasion we’re in a tent) or secured inside a building. 

By and large, touring bikes don’t garner a lot of attention when there are flashier targets around.

I use the same locks as Lyle has described but I have also for years always put my bike in the highest gear ( with my rolhof bikes) or with conventional gears high gear and taking the chain off when I 'park it'. This way if they are looking to just cut and ride it is much more difficult as many people have no experience starting and then riding a fully loaded bike.

We carry Abus Bordo 6000 folding locks (one each) and do our best to lock our bikes together and to a solid object if we must leave them out of sight when we visit a site (never in a big city of course). The locks aren’t light (1.3 kg each) but they are easy to mount and the two can lock together to make an extra-long lock. 

Our bikes are also each equipped with Knog Scout alarms/finders.

I used to use just a very thin cable and small padlock, which worked for 90% of situations as I tend to avoid cities. But it did keep me from entering the occasional museum or other city-place. Last tour I got a Tigr Blue, which is 480g. It seemed to be the lightest lock in the "gotta bring an angle grinder" territory. The main complaint I have is its holder seems a bit dinky; but I put it on my front fork with King Cage Universal Support Bolts, and added another short nylon strap for stability, and that worked out fine, kept it away from other gear but easy to access. 

My main theft deterring strategies:

1. Ride a type of bike that thieves don't know how to ride or how to sell.

2. Park out of sight from motor vehicles whenever possible. Trailheads, etc.

3. At restaurants, park the bike where I can see it from my table.

4. Lock the front brake with a hard-to-notice Velcro strap on the brake lever.

5. As a last resort I use a cable lock about twice a week during tours.