One hears a lot of stories about the magic of upgrades, however they do happen. In my experience, the best way to get an upgrade is to get a "guarentee" on a specific type of cabin. In this case you are not assigned a particular cabin, but are "guarenteed" that you will not get a lower class than you paid for, but could be upgraded. The guarentee seems to work best with lower cost cabins (inside/outside obstructed), but can work with any cabin. What it amounts to is that by not "locking up" a cabin, the cruise line can sell the same cabin (usually the less expensive highly advertised ones) over and over again. Each time bumping the "guarentee" passenger up to more expensive cabins. In this way a passenger with a limited budget will never be turned away because all the "bargain" cabins are filled up. A note of caution here--Never "guarentee" a cabin you would not be happy to sail in. The upgrade may not work out and you might get what you paid for! Also, if you MUST have a cabin low in the center of the ship because of a queezy stomach for example, a guarentee isn't for you because an upgrade cabin may be anywhere on the ship.
Another way to get an upgrade is to simply luck out and end up a ship that is no where near full (Doesn't happen too often these days). In this case, the cruise line will upgrade whenever possible to make as many people as possible happy. It is unlikely that one person would be upgraded six levels, as the cruise line would prefer to make six people happy (vice one) by upgrading each one notch with progressive bumps. Obviously upgrades are usually done in the last week or so before sailing and cabin numbers are assigned at that time. Hope this helps.