I have to add, though, that if you have all of the above and there is no lightning about, GO! Don't change your mind. The parks are usually fairly deserted in the rain. You can ride your heart out on ANYTHING that is open! And hey, hit those water rides. You're wet already. :) Gives you an excuse. I got to ride Loch Ness Monster at Busch Gardens Europe six times in a row without getting out on a rainy day.
So, in short, if you ride Thunder Mountain in the rain, have someone sit next to you or prepare your ribs for some pain.
On a side note, though, riding Splash Mountain in said Tropical Storm was simulataneously hilarious and awesome, and was the only time I have ever been asked at Disney if I wanted to ride again while still on the ride.
We had our light rain jackets that covered our bums and stayed in the parks the rest of the days. I remember a one ride cycle wait for Dumbo. The longest waits I remember for dark rides at Magic Kingdom.
Here is Los Angeles, rainy days are the best for the theme parks because almost everyone here hates the rain. I welcome the change in weather with open arms. If I'm not working and the rain hits, I cautiously hit the freeway and make way to the park of which I am a pass holder. I've done DL, SFMM, and Knotts all in the rain. I do recommend not riding "X2" in the rain. It's not a lot of fun turning face up into the rain after the first drop.
and interestingly :
Were the crowds any lighter ? No. It was June and it was packed out.
Although we did hear one man complain to his wife that he was getting soaked through while he was in the line for Jurassic Park River Adventure. Work that one out if you can.