When I moved to Chrome I tried to find equivalents to all the extensions I was using in Firefox, including video downloading managers, so I first had to switch to the 4.x Beta as the 3.x version didn't support extensions yet. But at that time there were no downloading extensions at all, as Google didn't yet release the APIs for that, so what I did was switching to FF (and waiting an eternity for it to start) whenever I wanted to download a video. Until one happy day, in Chrome I played a video I had already played some days ago, it instantly loaded! Which reminded me of the browser cache, I went searching for Chrome's cache folder, and there I found all the played videos !
Conclusion: To "download" your videos you just have to play them and you'll find them in the cache folder !
You will find a lot of files there with unrecognizable names and without extensions, so to spot your videos you can sort by size or by date, it'll be easier in Linux as it doesn't need extensions to display file thumbnail previews.
Chrome's cache folder in Linux :
/home/your_user_name/.cache/google-chrome/Cache
Chrome's cache folder in Windows XP :
C:\Documents and Settings\your_user_name\Local Settings\Application Data\Google\Chrome\User Data\Default\Cache
Chrome's cache folder in Windows Vista :
C:\Users\your_user_name\AppData\Local\Google\Chrome\User Data\Default\Cache
Chrome's cache folder in Windows 7 :
C:\Users\your_user_name\AppData\Local\Google\Chrome\User Data\Default\Cache
If going through all the files in that folder is frustrating, you can always use the extension Click&Clean that has a feature to play and save the videos present in your cache.