VLC is a video player (rather than an editor) but it does have a simple facility for removing unwanted parts of videos. You simply need to go to View > Advanced Controls to bring up an extra toolbar at the bottom of the screen. The left-hand button (red) is a 'Record' button. Play your video and, at the point where you want the edited version to start, click 'Record'. Click again when you want the shortened version to stop. VLC will then automatically save the edited version to somewhere on your computer. (In Windows 7 it's, unsurprisingly, the Videos folder. The location might be slightly different with other versions of Windows but a search for *.mp4 will always find it).
That suggestion isn't just derived from a bit of googling. It's the way I do it myself.
http://www.videolan.org/vlc/index.html