You can do this with Quicktime Player X. It's a bit clunky, but it's free and already included with your system.
Open up the movie you want to split, then press Cmd-T to enter trim mode. Then drag the in and out points to the piece you want. Hit "Trim", then Cmd-S to "Save As ". You then have to open the original movie file again and go through this process for each clip you want to split out.
If you happen to have Quicktime 7 Pro, the process is considerably easier. Just mark your in and out points with the "i" and "o" keys, then hit Cmd-C to copy, Cmd-N for a new blank movie, Cmd-V to paste, and Cmd-S to save. Then just close the new movie you made, go back to your original movie, and repeat the process. This way, you don't lose your marks or the frame you parked on, and can just step forward to the next frame and set a new in point. Odds are, unfortunately, that you don't have QT7Pro, but you can get it for $30 from the Apple Store.