There are lots of ways to download Youtube or Vimeo videos and save to your hard disk in Ubuntu.
ClipGrab is a free and easier way downloading and converting online videos from many sites like YouTube or Vimeo.

ClipGrab can download from the following sites: YouTube, Clipfish, Collegehumor, Dailymotion, MyVideo, MySpass, Sevenload, Tudou, Vimeo.

Downloaded videos can be converted to the following file formats: WMV, MPEG4, OGG Theora, MP3 (audio only), OGG Vorbis (audio only).

By the way, ClipGrab can also download HD videos from sites that have support for high definition (e.g. YouTube or Vimeo)

Install ClipGrab on Ubuntu

ClipGrab got a ppa ppa:clipgrab-team/ppa, you can read this graphical way adding PPA and install ClipGrab. Or just execute following command in terminal (Ctrl+Alt+T):

sudo add-apt-repository ppa:clipgrab-team/ppa
sudo apt-get update
sudo apt-get install clipgrab