Is there any free video cutter and converter for Mac that can handle popular formats like .mp4, .avi, .vob, .mkv etc.?
Some more alternative on our Best Mac Apps page, //www.makeuseof.com/tag/best-mac-os-x-apps/
As for video converter my personal favorite is MPEG Streamclip. Other popular choices are VisualHub, Miro Converter and ffmpeg.
As for video cutting and editing one option would be iMovie which ships [as part of iLife] with every Mac.
If you are running Snow Leopard or Lion (10.6, 10.7) and only need to cut at the beginning or end you can also use QuickTime X Player (the function is called "Trim" within the Edit menu).
The only other free video editing tool I know of is Avidemux,