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You cannot download video files on Nokia Lumia 610, but you can, however, stream supported videos by opening them in the browser. If you want to get a video file on your device, you'll need to transfer it using Zune or Windows Phone 7 Connector for Mac (can be downloaded on AppStore). Please see here for instructions on how to synchronise content using Zune.
Hope this helps,
thnks guys..... But it would be better if our dear nokia makes an video downloader free ..... Nokia is not as much supportive as it was :'(
As mentioned previously, there are YouTube downloader apps available.