With ScreenFlow you can record any part of your monitor while also capturing your video camera, iOS device, microphone, multi-channel audio device and your computer audio. It also has a built-in editor which is invaluable if you don't want to use a third-pary video program like FinalCut or Premier.
Camtasia offers a similar feature set with the ability to record your screen, webcam and also offers a feature rich video and audio editor which allows you to export your content seamlessly.
Soapbox by Wistia is a free Chrome extension that enables anyone to record, edit, and share high-quality videos in minutes.
Camstudio.org is able to record all screen and audio activity on your computer and create industry-standard AVI video files. Windows only.
Screencast-O-Matic is a Java-based screencasting tool that requires no local software. Works on both Mac and Windows.
QuickTime is included with every modern Mac and allows you to do screen recordings without any additional software. If you want to edit your screencast or add audio you'll need additional editing software.