THere are 3 different types of upgrades that I can think of.
1) the kind I think you are interested in is the free upgrade. No one here has been able to determine who gets these or how they are chosen. My observation is that cat 11 guaranty get the most upgrades (because
DCL can sell cat 11 rooms easier than cat 8 rooms - the 11's fill up, they bump a few rooms up and then sell more cat 11 rooms). These free upgrades, even though they are talked about quite a bit on these boards are really pretty rare. Only a few per sailing.
2) the second type of upgrade is the one that you have to pay for at the port. You can ask if there are any upper category rooms available, and if there are you may purchase an upgrade. The cost for this upgrade is usually less expensive than what the cost differential was when you originally booked you room.
3) the final upgrade path is the one where you book a room and decided BEFORE leaving on the cruise that you want a higher category room. You pay the full differential cost between your room and what it would have cost you to rent the upgraded room initially. I believe that in the past if you upgraded from a cat 9 to a 5 that you would have paid what the difference was at the time you booked the 9. Now I think that you pay the difference between what you originally paid and what the upgraded room costs today.
Bottom line, reserve the category of room that you will be happy spending the cruise in, because the free and reduced upgrades are few and far between.
edited to add: did it really take me 5 minutes to type this up - no one had responded when I started and Dr. Calvin's reply is 5 minutes before mine