I've gotten pretty close to "soaked" on the Pirates, but that was due to a fluke more than anything. In the scene where the ship is launching canon balls towards the fort, one of the up spouts went off and the water came down into the boat. It was wet enough that I was wringing water out of my shirt when I got to the bathroom afterwards. It's only happened once, but now I'm always paranoid during that sequence! On the drop, I've gotten anywhere from nothing to misted to more than damp, but not quite wringing wet...most of the time, it'll dry before the ride is over, but there have been a few times when there were still water blotches on my shirt/pants when I got off the ride. Like the PP mentioned, be sure to check the seat before you sit down.
There is the possibility to get wet on Matterhorn and Big Thunder. Both have a water splash at the end, but I've almost never gotten more than a few drops if any at all. There are a few points where the Matterhorn track goes by the waterfall and it's possible to get misted (depending on which way the wind is blowing) and Big Thunder has a water fall at the end of the first big climb (I've never gotten "wet", but it's possible to get dripped on).
As a PP mentioned, the Pixar Play Parade has a water element and some areas will get wetter than others. It's kind of random (I think), but if you're in the front row (or two), be prepared to be squirted. I don't think most folks will get soaked (i.e., wringing wet), but if you're in the wrong spot, you can get pretty wet. The girl two down from us got one of the squirts full on and she was close to Splash level wetness (at least in terms of number of water blotches on her clothes).