We started taking our annual WDW vacation in late August when our now 18- year old daughter who is in her first year of college started High School in 2003. My youngest 2 daughters are 13 and in Grade 7, so we are finally getting an April trip in a few days -

. Once they start HS in 09 we will be back to late August only.
Here's a second for going in very late August or early September. Generally, if your kids are in elementary grades, you can probably get away with missing the first week of school after Labour Day - we did that in '06 where our son missed the first week of Grade 1. It didn't seem to cause any problems at all.
This year we are planning on going until Labour Day itself - flying back on the Tuesday. This will mean that he misses the first day of Grade 3 - again, shouldn't be a problem.
Once kids are in high school - some can miss a week, especially right at the beginning of the year, without a problem. Others, not so much. If you can book the last week of August, that can be one of the best times to go - but there are still drawbacks. Benefits include the fact that one of Disney's best promos (Free Dining) has included at least the last full week of August (except for the Bounceback '08 offer), and since most schools in the southern U.S. have been back in session for about a week or so, the parks are less crowded - the week after Labour Day is even better for low crowds though.
The drawbacks - it IS hurricane season. While this won't likely affect Disney World itself - the risk is flights in/out of Orlando being delayed or cancelled. We've gone twice during hurricane season though and had no problems.
The second drawback - the HEAT! The humidity is just gross. But, if you are smart and get to the parks first thing as the open, have an early lunch, take a break in the afternoon and return after dinner, you can often avoid the worst of the heat and the longest lines of the day (from about 11am to 4pm).
In some ways, we would rather go at a different time - when the weather is better - a little less hot, but still great for swimming there, and when there aren't hurricane risks. BUT, those times would require our kids missing school during the main part of the school year, the parks might be busier (definitely the case during March Break and Christmas break), Free Dining would not be offered, and some of those times will be during higher rate seasons.
Considering all the options and the pros and cons, we feel that a late August or very early September is the best time for us - it works in terms of school, cost, and park crowds.