1. The most universal kind is a joint based on two overlapping circles. Rotation pivots in the circle's center and therefore the joint never breaks.
This is probably the most widely used type, because it does not require any special attention or additional clean up.
The drawback is the clearly visible rounding of the joint, which is not always desired stylistically.
2. Variations of the circular joint exist where the overlapping circles occupy only a part of the limb surface, while the rest is asymmetrical. This can yield more natural organic looks.
The drawback here is that such joints have a much smaller range of flexibility and the elements often need several different states inside the containers to make them look natural at various angles.
3. The third type is an angular joint, which is not based on a circle. The elements meet at a point and that's it. Stylistically it can have specific appeal, but has the disadvantage of needing multiple states of the elements inside the container. Also the limbs may appear shorter as they bend, so some correction of length might also be necessary.