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FVD Video Downloader
To be honest, this extension is a bit of a disappointment. It will grab videos and files in many cases, but not all. In particular, it refuses to download YouTube videos. Now, why would I want my own copy of YouTube videos? Well, I often download conferences and meeting videos, as well as technical discussions, bring them into VLC Media Player, and play them back at 2x speed or more. It makes it possible to get through a lot of material quickly.
Since FVD Video Downloader won't download YouTube, I find myself going back to Firefox to use the Download Helper, one of the few add-ons I still use Firefox for.
How often used: Rarely.
Live without it factor: If it would download YouTube, it would be a regularly used tool. Without that functionality, I can live without it.