Our first trip was late September and I would definitely visit at this time again, if I was not now tied by school holidays.
The crowds were really low and most rides were "walk straight on". On some of the rides, including Big Thunder Mountain we were able to ride twice without queuing.
The only possible downside is that some of the park restaurants are not open everyday. There is such a selection of restuarants in the parks and Disney Village that this is really only a very small problem, if a problem at all.
The thing that we liked most about the end of September was that the park was getting ready for Halloween and every day when we went in to the park we spent our time trying to spot want had been added overnight.