Application of Inverse Kinematics

(a) skeleton of a head-less monster; 
(b) added an additional link for the head, which is made to follow in its direction the movements of a bee; 
(c) skeleton on a bicycle; inverse kinematics is used to keep the feet on the pedals and the hands on the handle bars.

There are many more issues:

How to make the "most natural looking" animation of a skeleton moving from one state to another one.
Inverse kinematics in the presence of constraints (e.g. limitations on joint angles; keeping center of gravity above feet).
How to maintain stability at all times (step-size control).
Interpolation for smooth animation (especially in the presence of constraints).

To learn more:

(This is material that you should look at if you choose I.K. as your project extension,
  but it will not be on the Final Exam.)

Numerical Methods for Inverse Kinematics, by Niels Joubert, UC Berkeley, written for CS184.

Also, play with the IK solver to demo applet:  http://www.eecs.berkeley.edu/~jima/ikdemo/

A. Watt and M. Watt:  Advanced Animation and Rendering Techniques -- Chapter 16.

Lecture 18 by Prof. James O-Brien, Fall 2008

A more detailed presentation by Bill Baxter, UNC.