It depends.

Or just games in general...

http://en.wikipedia.org/wiki/Inverse_kinematics

But its the same problem as generating terrain procedutrally, that to generate something realistic you have to involve limitations (like there are only certain ways the human body can bend and how fast)

As well as the actual movements for an 'action' may have many sub-goals (like when you reach into a pile of stuff to extract one item - reaching around some things or when pulling, part of the goal is to pull with force along a certain vector for the target object (realer physics for the whole world system).

So your body is a complex tool that has to work only certain ways (and even more resticted ways to act efficiently) and then have the motions work in relation to other objects -- which if THEY in turn have complex behaviors require even more special specific movement (putting a spin on a tennis ball to achieve a curved trajector that puts the ball on the court where you opponent is NOT going to be)

SO considering all that complexity, you probably would employ some kind of Planner AI to solve all those simultaneous problems to make your figure move in a 'realistic' fashion.

With a dynamic situation this all then has to be done often in near real time.

Thats not even counting deciding beforehand (or along the way or adapting to the current situation/state) WHAT the higher level goals of the movements are in the first place.

Now compressing motion data using equations versus bone time/angle tables (versus tweening keyframes) could be very useful when you have lots of objects and a limited data bandwidth (all precalculated data) could be quite important as World complexity increases.

I suppose with data streaming, through server, you could add dynamic motion data creation by the server or for each avatar by its own client, which then is sent upstream to be distributed to other multipile clients(multiple viewers of the same action).

OR

Semi static generation (by server ) to make various reused action animations change over time with different variations (keep 3 or 4 different ones cached so objects in the same vicinity doing exactly the same high level thing would do so with some variation) Pipe the (hopefully nicely compressed) equation/coefficient data to the clients.