Updating Programs With Active Antivirus Installed

This has been bothering me for a while, microsoft and many other companies offer every once in a while updates to their programs, adobe office, explorers etc. If I have an active antivirus program, how important is it to always update, for instance if the update is a security update. If I have a computer that I do not surf the net, only work on, but I transfer files to another computer back and forth with a usb chip. Or another example, if I connect the above computer only through outlook to get emails, do I have to worry about always updating microsoft office or adobe programs. Of course my antivirus is always updated.