All the rides have different tolerances for rain and bad weather. Nearly everything (all the coasters, Power Tower, Demon Drop, etc) will shut down in lightning, and must remain closed until the lightning is well and truly gone. As for rain, some of the first rides to go down will be the Wildcat and the Demon Drop, others vary. Iron Dragon will go down to clean out the "diapers" between the cars that would catch the water, but most of the coasters can operate in rain pretty continuously. If it is raining too hard, obviously, it becomes painful to ride, and they're closed.
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PO!NT OF VIEW - A Different Look at Roller Coasters
http://www.crosswinds.net/~justmayntz/thrills/