The father of insane inventions, a brilliant but lonely man with a hairless cat or dimwitted assistant. That is the image which comes to mind when I think of the Mad Scientist. It is a trope that has been exploited in countless films and cartoons, and more than half the time, the Mad Scientist is also the villain. Aside from visual representations, other characteristic traits that Mad Scientists share includes an unfortunate past/some sort of event that made them how they are, isolation or rejection from society or the science community (probably due to ethics violation), and misguided but good intentions. Using an example more recent in memory, I would say that Dr. Frankenstein fits the trope of the Mad Scientist; the death of his first wife put the idea in his head, and even though the medical community frowned upon it, he still wanted to bring the dead back to life.

And another commonality in the Mad Scientist archetype? Their end is always brought on by their own creations.