Many websites feature online video editing applications that allow you to edit videos online. These apps are not as feature-rich as editing software that you would install on your computer, but they do allow you to do simple video editing right on the web.
YouTube video editing software doesn't offer all the features that some of these other online programs have. But it does give you the opportunity to easily edit videos that you've previously uploaded to YouTube. Given the popularity of YouTube, any editing features are better than none.
Adobe Premiere Express is a stripped down version of Adobe Premiere, designed specifically for online video editing. Used by major sites, Premiere Express is the leader in online video editing. It's easy to use, free to get started, and offers the convenience of being able to edit your footage online from any internet connection in the world.
JayCut online video editing software offers unlimited online storage for your video files. Upload everything you want, and edit it online using the JayCut software. The editing capabilities are fairly complex for online software, including multiple video tracks, video effects and music.