I just wanna say right now how awesome this idea for a thread is.
Umm... I have read some Jim Carrey interviews and I think he does method acting. In the DVD commentary for "Bruce Almighty", the director talked about two of Jim's crying scenes. In one, where Jennifer Aniston think he's proposing to her, he did multiple takes (maybe 10 takes?) and was able to bring on the tears every single time (the director was quite impressed!) Also, when they shot the scene where he's walking in a downpour, there was just one take and he got the "right" emotion right away. I also seem to recall that for a crying scene in "The Majestic", he prepared for the scene by being alone for a bit and quietly tinkling on a piano (obviously there was a piano handy on a nearby set). I believe it was the scene where he has to say goodbye to his dying "father". Also, in Eternal Sunshine of the Spotless Mind, the director was ready to use fake tears on Jim, but Jim refused as he wanted them to be real. Apparently the tears didn't come right away and they were all waiting (perhaps somewhat impatiently?) for them to come, but finally they came (the scene is where he's in some kind of altered state where his mind is being controlled, so I bet that's why it was harder to get them to come... not a 'natural' type of crying scene at all, but more of an eye watering while wearing an expressionless face kind of thing!)