When we watch a flv file in Chrome browser it is getting buffered at location defined by Windows Environment Variable: %TEMP% as fla*.tmp.
Now how can we save this:
Case-1:
If buffering is complete. Then don't close the browser. Copy the fla*.tmp, this locked by Chrome. Thus we can use HoboCopy to copy it. As below:
C:\HoboCopy.exe %TEMP% C:\FLV_FILES fla*.tmp
Case-2:
If buffering is not complete. Which means browser closed before complete buffer download. Then flv is stored at: C:\Documents and Settings\USER\Local Settings\Application Data\Google\Chrome\User Data\Default\Cache. In case of Windows 7 it is: C:\Users\USER\AppData\Local\Google\Chrome\User Data\Default\Cache. So just open this location in Explorer and copy the files flv files (starts with f_* and does not have .flv extension at the end). After copying to desired location, rename it to .flv.
TIP: I normally sort according to size in Explorer and copy files which are considerable size few MB's at least, to avoid copying the small files which may not have video content.
Try this technique. You don't need any download plugin etc. This is not restricted to YouTube it works with other sites as well.