Solution1 - :
Well, the first solution is to use softbody SplineIK with springs. This however would be almost entirely automatically animated, meaning that you would have very little control. So you would not be able to create specific poses as well as let the softbody dynamics run. You can get around that by animating the weight of the softbody and using shape animation on the spline. However, this is very combersome.
solution 2 - :
This is gonna sound a little complicated, but it ain't really, and works very well. Firstly, heres the big key to all delay systems and flocking systems :
you need to tell the computer, via an expression, that one joint will match the rotation of the root joint, so many frames behind. So, here is a simple example :
float $offset = 1.5;
j2.rotateX = getAttr -t (frame - $offset) j1.rx;
j2.rotateY = getAttr -t (frame - $offset) j1.ry;
j2.rotateZ = getAttr -t (frame - $offset) j1.rz;
you will need a different offset for each joint to create fluid like delaying motion, so effectively, one joints rotation follows from the previous. You can right a simple mel script to create the expression rather than type it all out yourself.
What I find quite useful is to add an interactive stiffness control. This is very simple. Rather than create a specific different offset for each joint, you can make the offset value simply an attribute of another object or e.g. the translation in Y axis of a locator, and then add a different multiplyer for each joint instead. This way, you can animate easily when you want the flowing joints to be stiffer or floppier or even more turbulent as if being blown by wind. e.g :
float $offset = locator1.ty;
j2.rotateX = getAttr -t (frame - $offset) j1.rx;
j3.rotateX = getAttr -t (frame - ($offset * 1.5)) j1.rx;
j4.rotateX = getAttr -t (frame - ($offset * 2)) j1.rx;
etc etc
now this obviously won't give you accurate control of the tenticles enough to set specific poses. So what you can do is combine the follow value with IK. In brief, create an IK handle for each joint to the next, group each one individually and move the group-pivots to the end of each joint. Now create a particle object snapped to each joint. It will have to be multiple particle shapes with just 1 particle each. Match the pivots of each particle to each IKhandle. Now you need to obtain the worldposition of each particle (not the shape node) which you can do through another expression ...if you need that expression, email me. Now all you need do is exchange the rotation attribute in the "follow" with translation instead, and rather than set the joints to rotate, you will now be using the particles translation instead. So, the particle placed at joint 3 will follow the particle at joint 2 and 1 respectively, etc etc. You now need to constrain the group nodes of each IK handle to the individual particles using the worldpositions.
All you have to do to animate it now, is to animate the particle at the end of joint1, which will move with the body if parented to the head joint for example. The tenticle will now flow fluidly and believably, you have direct control of the floppy/stiffness as well as the stretchiness (for cartoony effects) and to set a specific pose, all you need do is animate the particleShape nodes that are parents to the particles. Et Voila 
Have fun and experiment.
~Pootang the Great~
