What is the best method of printing joints for action figures? I'm interested in 3D printing toy action figures, but what I don't quite know how the joints should be designed to allow flexibility. 

I could imagine maybe something like a screw and nut for the arms and legs that are separated with a hole in the middle that can join them, but I don't know how to get a wider range of motion on shoulders and hips.
(NOTE: Converting comments to an answer.)

An interference fit would probably work. There are a couple of styles I can think of which would do. Here are some ideas from thingiverse.com which may work for your needs.



(image taken from this design by OgoSport)

With this style of ball/socket, you'd have very good articulation. More than enough movement to allow for a posable action figure.

Another idea from thingiverse.com is this:



(image from this design by NEMO_from_saturn)

The idea behind this style of joint is to insert it into each part (part fits over the end). This is premade and would be easy to utilize. The thing about this is, they are covered by the licensing involved with patterns found on thingiverse. 

As with anything printed or mechanical, it will wear over time. You won't ever get anything which doesn't wear. It's just a fact of how it works. Some printed filaments will have better wear properties than others, like ABS, NylonX (polyamide with chopped carbon fiber strands), nylon, PET (PETG/PETT), or polypropylene (this is not all inclusive). Each filament has its own printing properties and idiosyncrasies, so pay attention to what needs to be done to print with them. This doesn't mean all of the parts need to be printed out of this material, but rather if using a joint (like the second image), you could print it out of the better wear material and print the rest out of filament which is cheaper and is easier to work with.