I've started to do a lot of screencasting at my job. I probably make 2-3 screencasts per week. Here's a brief rundown on what I use them for & the different software packages I've tried.
Computers are Hard
It's impossible to explain how to do anything on computer. "Click the glowing blue circle in the bottom left, drill down until you get to Microsoft Office, then select Excel, which has a green letter X on top of an spreadsheet for an icon." The next step will certainly be worse, given Microsoft's ribbon UI. It's a lot easier if users see a particular action performed.
Sometimes when I find a bug in a website or application, I'll just make a 1-2 minute video & send a link to the appropriate party. It's much more useful than ranting. I really wish, when people run into problems with our website, they would do the same. Little things like what browser version can make a huge difference & are rarely reported along with problem being experienced.
Screencast-o-matic is a Java applet, so it runs in the browser and works on any platform. It's biggest advantage is that it highlights your mouse with a big, bright yellow circle & clicks cause little blue ripples. Videos can be uploaded to a linked YouTube account or the screencast-o-matic site. The video quality is not great & there usually ends up being a lot wasted space. Small watermark in the lower right corner.
Screenr is another Java applet which hooks up to YouTube & its own publishing site. It does not highlight your mouse but the videos are of decent quality & the Screenr site itself is quite nice. I would recommend either of these first two options.
Quicktime (Mac) allows screen recordings (File > New Screen Recording) which is nice in that every Mac comes with free video editing software (iMovie), so suddenly you're in business. There aren't any mouse highlighting options & the on-screen keyboard for Mac is pretty useless, however.
CamStudio (Windows) is open source & gives you a few extras like custom cursors & some post-recording editing.
HyperCam (Windows) lets you highlight the mouse but most of all, it's the only software here that lets you pop up a dialog which displays every key you press. That may not sound important but when you're trying to teach keyboard shortcuts, it's vital. Its UI is clunky & finding the menu for displaying keystrokes near impossible; consult the great Google.
Neither of the above seem well-maintained but they run OK on Windows 7.
Jing (Mac/Windows) is probably the most well-known screencasting software but it's started to frustrate me. While it works fine, Jing puts a pay wall between you & YouTube (I cannot for the life of me find a way to take its .swf output & upload it...would love to be proven wrong here) & offers no advanced features like mouse highlighting. It's quick & it gives you a screencast.com link right away, which is fine for one-off videos sent to individuals or small groups, but it's useless as a publishing medium. &, while I'm on it, the UI messes with my expectations in annoying ways (an icon of two computers means History? a stop-sign with a hand in it means Quit? I have to click three buttons to quit?) & the screencast.com admin page is buggy.