It is more than possible: Go to YouTube home page, click 'Log In' (or - if you do not have an account, click 'Sign Up' and register), find the 'My' heading and click 'Playlists', select 'Create Playlist', write a name, description and tags you would like to include, choose whether you want the Playlist to be public or private, click 'Save Playlist Info', add as many Playlists as you choose and add Content to your playlist.
The adding action is done as following: click the 'Videos' link from the Playlists page, or the YouTube logo, browse through the available content and locate a video you would like to include in your playlist, click the video, select the 'Save to Favorites' text link, find the 'Select a Playlist' pull down menu under the 'Add Video to Playlist' heading, choose the Playlist you'd like to add the video to and click 'OK', click 'Playlists' at any time to view the content saved in each Playlist you have set up, and use the 'Share This Playlist' button to send to friends.