2010 edit: This is, again, a very old post, and I had pretty limited experience with 3D at the time. It's kinda silly stuff, looking at it today, but basically, it tries to explain something with the wrong words. It's talking in fact about how nice and easy it is to get proper curves from a hierarchical FK output, and how IK forces you to create curves with some sort of spline interpolation, when you animate. Basically, between 2 positions of an object, you can have all sorts of interpolations, like linear or spline and so on. While a hierarchical FK rig uses rotations, and not interpolated positions, so of course the result will be nice round movement. But it's a matter of setup logic, and there is no problem with IK. Well, IK does have a problem though, the IK pop... :P that's still around here even in 2010, and I don't see any rigs out there managing to bypass it. Houdini (the 3D app, not the dead guy) has an awesome damping solution that can be... creatively... used in rigging and gets rid of the IK pop, but in Maya, a.t.m., except for a certain Elastik IK solver that is not updated anymore, I couldn't find anything, or any technique that would fix the problem.
IK, or Inverse Kinematics, is a wonderful technology that comes with a huge problem (ok, there more, not only this one): its interpolation. Still, pretty much all rigs include it. In my humble opinion, this is dangerous territory...
Yes, it's a matter of choice and of how you use the rig, the technology... but! There's a big "but"! As Keith Lango said it in a famous tutorial... "Linear is as Linear Does". Human motion is not linear (motion of all kinds, in general, is not linear, except for that of... some robots...), and working with straight-lines-only makes your work harder: you're trying to get rid of the linearity and it's hard, real hard (ammmmm, aaaand... I've seen quite a lot of animation where people didn't even bother trying to make things not look linear, they just accepted the IK-generated-output blindly and didn't correct the extra-funkiness: flipping, weird contortions generated by the linear IK interpolation, linearity in general).
An FK rig in movement on the other hand is normally arched, logically predictable, and hierarchical, all 3 attributes being, I think, essential to a natural flow of motion. Now some people prefer to pose with IK, some with FK, some with a combination of both, but the issue here is not with the posing, it's with the keying! It's an issue of what happens when you let the computer inbetween, as obviously you will have to, unless you plan on keying every single frame.
Here's a drawing that shows you a simple chain with IK (ugly) and FK (natural) interpolations:
Posing with IK has the added ability of more or less... locking a joint to a point in space, which is something you need to do by hand with FK (counter-animating is always nasty, but I think there's less counter-animating in an FK-workflow... but that really depends on the workflow of each animator). So, a combination of posing with IK & FK (again, I think IK can actually need more work, more cleaning necessary, more counter-animating - like "taking the long shortcut") and keying FK only (!!!) might be ideal... as far as I can tell... Just make sure all them IK handles snap back to joints and are not constrained or parented (so you don't lock them in space).
Edit:
For quite a long time I had the wrong idea that f-curves tweak timing, when in fact they tweak values that affect both timing and spacing (in the old days I was not an f-curves fan, but once I got used to them and used them more and more they became an essential part of my workflow, I had the wrong idea that it would be best for an animator to work purely visually and set as many keyframes as possible... that's stupid, smart use of f-curves allows you to control your animation with a minimum number of keys, which is not a bad thing in fact, it doesn't make animation more artificial, just simpler to control. you can make easy changes to your animation and make sure everything flows well fairly easily. so even if one animation curve is very simple, when 10-20 different animation curves overlap, a rich polyphony is born, and the result looks organic). lK handles don't move in arcs, but when we use spline interpolation, we do get rounder spacing, not an arc, but also not a straight line. The problem in the above example doesn't always happen, only sometimes. Actually, a greater problem of simpler IK rigs, as far as I can tell at the moment, is that they usually don't encourage twisting articulations, and so animators who prefer to work within the limitations of the full-body IK rig tend to use very little twist in their poses. The result is that a straight body, with little or no twist, looks stiff and robotic. I'm currently working within Motion Builder, and MB's rig allows great flexibility and you can twist to your heart's delight; even though it's a full-body FK-IK solution, it's rock solid :)