Trigger to UPDATE after UPDATE?

Question

I want to make a trigger to record the time of any update as:

CREATE TRIGGER col_update
AFTER UPDATE ON col
FOR EACH ROW BEGIN
UPDATE col SET updated=NOW() WHERE id=NEW.id; // or OLD.id
END

The problem is that when this trigger tries to update the updated column, it is also another update event, which runs the trigger. This will create an infinite loop, which does not work.

How can I store the update time in the corresponding column?

I wish to use a trigger because there are many columns in the table. If I try to set the update time manually, I would need to modify many queries.