If you're looking for a simple, one-click solution for converting and downloading YouTube videos sans software, DownloadTube is a free tool for web-based YouTube file conversion.
Copy the URL of the video you want to convert, visit DownloadTube and paste it in, then select which format you want. DownloadTube can convert YouTube videos into MPG, MOV, 3GP, MP4, convert it to an audio-only MP3 file, or grab the native FLV flash file for you. Click "Convert and Download" and the file is converted and saved to your computer.
DownloadTube is a free site and requires no registration.