I have MPEG video (.mpg) that I would like to convert to FLV format for use in Flash players. What is the easiest (idiot-proof) way to do this on a Windows machine?
FFmpeg is available for windows (even with a GUI!) and does exactly what you want.
You could use Zamar (http://zamzar.com/) which is online, or Any Video Converter (http://www.any-video-converter.com/products/for_video_free/).
I've used Any Video Converter and it works well. It contains components of FFMpeg and MPlayer in a very nice, easy to use interface. You can download it here: http://www.download.com/Any-Video-Converter/3000-2194_4-10661456.html
Mediacoder is a nice program to convert almost anything with a nice intuitive graphical interface.
Use FLV Converter. It has both standard and portable versions, and it's freeware.