We were there July, 17 - 22, 2001 and it was hot, humid, and rained everyday from about 3-5pm. That being said, it was still an awesome trip. The key is to be prepared. Bring a bunch of bottled water to WDW with you, rent a fridge, and store the water in there. Everyday, before you head out, load up a back pack with water bottles to use throughout the day. (They cost ~$2.50 in the parks.)
As for clothing, wear light colored, loose fitting, comfortable clothes, a hat, sunglasses, and comfortable (and not worn out!!) tennis shoes (this is VERY important).
Get an early start every day. Try to do EMH (Extra Magic Hour) parks everyday and go until about early afternoon. (1:00 or so) By then, things will be really heating up and the parks will start getting crowded. Go back to your resort and take nap and a swim. You'll be surprised how much the nap helps you. Go back out about 4:00 - 5:00, hopefully by then the rain will be about over, and stay in the park until it closes. The nice thing about summer is that there are long park hours.
This is the plan we followed and it worked great for us.
As for crowds, yes it will be more crowded then mid-September or early February, but it's not a zoo like Christmas/NYE, Easter, & July 4. The kids may all be out for summer, but they are not all there the same week!
Have a great trip!!!