The answer will depend on your physical capabilities. So I will throw out a few options.
A trackball or touchpad can sometimes work for a bit, but those require decent finger movement which usually doesn't last very long. You could use a trackball with your feet, but not sure how easy that would work.
There are a couple options to use a web camera and free software to control the mouse with your head. Do a search for "eviacam" and "cameramouse". Your results with these will vary, and is not a robust solution in that you can expect to need help from someone when the software loses track of your face, which is practically guaranteed in most users experience. But the price is free if you have a webcam.
A robust headmouse solution is the Naturalpoint SmartNav EG. This uses a small reflective sticker on your forehead, glasses, hat, or whatever. A sensor placed on the monitor tracks the sticker. It is quite precise, and many folks have good luck with using it.
There are also foot pedals that can replace the standard mouse buttons, such as the Kinesis Savant Elite, although there are other styles too.
I'll also point out the some other free software named "Point-N-Click" and "ClickAid" which can help use any type of mouse, including a standard mouse, if the problem is more with clicking instead of moving it.
While not really mouse replacements, it is good to also check out "Point-N-Click" and "Dasher" forwhen the keyboard becomes a problem.
Hope this helps.