Personally, I do not do video editing on Linux — for that I use Apple's iMovie. :) For those who prefer working on Linux full-time, like Mr. Hartley, his article will give you an idea what applications are available on Linux in as far as video editing is concerned. Mr. Hartley reviewed four video editing applications, namely Kino, LIVES, Cinelerra and MainActor. Unfortunately, not all four apps are open source.
For a second opinion, check out "An Overview of Video Editing on Linux".
[image courtesy of KinoDV]