Although I personally think that Camtasia is one of the best software for creating screencasts the below are a few of my (free) favorite apps when I need something quick:

• Screenr: It’s meant to be used with Twitter but once you save you have the option to upload to YouTube or save it as an mp4 file. You can also embed the video onto your blog or website or just share the URL via email or other methods. One note: If you have multiple mics plugged in to your computer don’t forget to select the mic input first before you start recording or you’ll end up with no audio like the same video I linked up above.
• Jing: By the same company as Camtasia. Like Screenr you can only record up to 5 minutes. But it does a great job and besides videos it creates screen captures too (the Screenr screen capture was taken using Jing). The image/video (png/swf) can be saved directly to your computer and the quality are quite impressive for a free and simple software.
• CamStudio: Use this tool if you need to create an AVI video. You can also export the AVI to an swf file right in CamStudio.

Which do I recommend? It depends on what you need. If you need a video to quickly post to Twitter, Screenr is the way to go. If you want a video that you can save to your desktop in swf format I’d go Jing. If I need a 6 min. video or a video in AVI format, I’d choose CamStudio.