rain: The condensed moisture of the atmosphere falling visibly in separate drops.
reign: Hold royal office; rule as king or queen.
rein:A long, narrow strap attached at one end to a horse's bit, typically used in pairs to control a horse in riding or driving. Cause (a horse) to stop or slow down by pulling on its reins.
If something is out of control, you do not rain it in. You do not reign it in. You rein it in.
Seriously, I've read two scholarly books in the past week that used the phrase "reign in." It bothered me more than the book on phenomenology that used the phrase "irregardless."