Links to Online Videos of Good-Quality Lectures by Mathematicians

The audio isn't great but Serre's "Writing Mathematics Badly" is classic. It's a discussion of what is and what is not good mathematics notation, style, etc. It also has quite a bit of humor mixed in:

Part 1

Part 2

Part 3

Let me contribute by posting the following links:

Part 1

Part 2

Part 3

Part 4

Part 5

Part 6

It is a talk by Paul Cohen about his work on the Continuum Hypothesis and his interactions with Kurt Gödel. This talk took place at the Gödel Centennial conference in Vienna in 2006.

Here is another video (high-quality video this time!):

Benoit Mandelbrot: Fractals and the art of roughness.

The title pretty much explains itself, I think. It is intended to explain fractals and chaos to the lay audience.