TechSmith's Camtasia Studio 5 is one of the best known and used products for screencasting (recording your computer screen and frequently audio at the same time). Like many really useful software packages, it's expensive, but it works very well.
Camtasia makes it ridiculously easy to record a window, or a specific area of your screen containing multiple windows, along with your microphone so that you can narrate whatever you're doing. It makes it very easy to record tutorials or to show someone remotely how to do something on the computer, or to record someone on your computer to demonstrate to other people later. It has a variety of other uses, but this is primarily what I use it for.
It's extremely user friendly and the default options are appropriate for most users. It's as simple as starting it up, clicking a window (or dragging over a rectangular area) and hitting record. When you're done, click stop and Camtasia preprocesses the video and audio and presents you with a variety of output options including standard video file types like AVI and MOV, as well as stuff ready for streaming over the web like FLV/SWF. You can define how rich the audio should be as well as the resolution of your video to decrease the file size.
The only drawback is that it can take a long time to convert and encode your video. Depending on the resolution and how long the video is, it can often take hours to prepare a 60 minute video, although this is a general time issue you have to deal with in any video recording/converting application. If a video isn't done right, you can always reencode it, or save it for later to be processed at a future date.
Customer service is good, although I haven't needed to bother them about much. When you pay for an expensive software product like this, you typically expect and get good customer service.
Overall I really like Camtasia and I use it frequently. It's very easy to use and I could probably give it to my mother and within 5 minutes of simple instruction she could be using it. The price may be a bit high, but in this case you really do get what you pay for.