There's no magic answer to your question. The only general rule I know of is: The lower the hotel occupancy rate when you stay, the greater your chances. We've been extremely lucky with the upgrades. We've been upgraded 5 out of the last 6 Disney resorts we've stayed at. By "upgrade", I mean we were given higher level of room than we've booked... no suites, concierge, etc. But then again, on these visits we've gone in January or mid-May when things are slower.
Only twice did we "ask" for an upgrade. The first time we were stayed in POFQ and our youngest was less than a year old. We faxed the room controller and my wife said it would be nice if we could have a room facing the pool so she could watch the older kids swim from the room while the baby napped. We'd booked a standard view room, but such a pool room was an upgrade. They granted the request.
The second time was in May 2002. We stayed at the Dolphin with my wife's Teacher's discount. My wife and kids waited behind me in the lobby while I checked us in. I told the clerk "I've stayed here on business before (Jan 1997), but this is the first time my family has stayed here. Anything you could do to make the stay special for them would be fantastic." She checked a couple of things on her computer. Then excused herself and went behind a door. She emerged from behind the door with a manager in tow. He informed us that the Dolphin was running a special program during the 100th anniversary celebration of WED's birth. They were select two families from each state as "Honorary Check-ins". They had selected us as one of the Michigan families. We were given a "resort view" room, a large plush Mickey, a 100 Years of Magic pin, and they took our picture.
Our last visit was in mid-June of this year. It was just my wife and me on a second Honeymoon. It was a busier time of the year and we didn't have the kids with us. For the first time, at WDW we didn't get an upgrade. But we weren't disappointed. The thing to remember is to expect what you paid for, and be tickled when they grant you more.