1. The traditional French Squat-on-Ceramic. Nice little footmarks moulded into the ceramic so you can position your feet not to get wet. No splashback. Bit awkward I imagine for the old or disabled.
2. Whilst not concerning the "big one", only public "small ones" for men, French pissoirs were often architecturally pleasing. Has anyone ever done a photostudy?
3. The "pit latrine": widely encouraged in the developing world by the likes of the WHO and that marvellous work Where There Is No Doctor for rural healthworkers originated by David Werner. Basically an approximately 2 metre x 2 metre hole in the ground with a reinforced top with a hole over which one squats. See how to make one here.
It can be more or less sophisticated.
In Nyala, Darfur, being dry, we shared a fenced-off open-air pit with the owners of the courtyard. And it being a Muslim household, no problems with toilet paper quality - jug of water and bar of soap next to the pit. Wash with your left hand and eat with your right.
Here, where it rains, sheltered pit latrines are recommended and there have been UN/WHO projects to encourage the local population to construct them - "we'll provide the materials if you provide the labour". I have my own.
A vent is recommended and a simple wooden cover for the hole. You can design the top as you like - I have known someone install a regular European toilet bowl over a pit and then flush it with a bucket of water.
4. The "bucket-drop". I have come across these in both Darfur and N.W. China.
Basically you build a raised holed platform in the outside wall of your courtyard and you defecate into a bucket which is accessible from a "cubicle" on the outside of the wall. Then the nightsoil collectors (the worst job in the world?) come round and collect the contents of the bucket. If they don't come frequently and regularly or you have a large family , the bucket soon becomes fly-ridden overflowing mess.
However, in colder climes during winter this isn't too much of a problem.
In the college holidays of the winter of 1981-82 I toured northern China and visited the famous Buddhist decorated caves of Dunhuang in north-west Gansu province near the border with Xinjiang or Chinese Turkestan (hmm ... another story there).
The local state-run guesthouse was pretty rudimentary. Temperatures were constantly sub-zero, the bucket-drop toilet was across the courtyard. Going outside to relieve oneself in the middle of the night was torture. Looking through the hole of the bucket-drop was a metre high pyramid of offerings. Couldn't see a bucket - was there one? Ones offering froze on contact. I guess being a nightsoil collector was seasonal employment!
5. Anywhere ...
So let us finish herewith my scatological offerings and move on ...