Go to the cruiseline's website, and follow the process as if you were going to purchase a cabin. Where it says "type of accommodation" click on balcony, or inside, or suite, or whatever. I also consider a cruise sold out if the only thing left is the President's/Owner's Suite that costs something like $17,000 per person. If you play with it for a minute or so it's pretty easy to find out what type of cabin is still available.
BTW, as noted previously, I goofed on the date at the beginning of this thread. The cruise was actually for 2004. Last year Princess had only two departures with that itinerary, and both sold out quickly. In 2005 they've dedicated a whole summer of departures on one ship to the Greek Isles so they shouldn't sell out so quickly. Of course, the trans-Atlantic cruises are only twice per year per ship, but those tend to sell slowly, and good bargains are to be had even on the last sailing of the regular schedule before crossing. For instance, there were several couples on our Greek Isles cruise who had lots of spare time and who snatched up real bargains by agreeing to stay on for the crossing, ending up in Ft. Lauderdale. It helped that Princess had arranged their air initially. Of course, they had to change cabins; they packed up and the cabin boys moved them while they were out sightseeing for the day.
Charlotte