Man of Steel:
According to
http://ga.water.usgs.gov/edu/sc2.html you need 26,067,840 gallons to rain down to raise the water level 1.5 inches over one square mile. I'm picking this number, since according to Wikipedia that's the highest level of rainfall recorded, per minute. Let's assume, for this discussion, that that much water came down, per minute, across the entire earth, which has a surface area of approximately 196,939,900 miles
2. That would mean that 5,133,797,802,816,000 gallons would be coming down, every minute. That's more than 1.5 times the volume of water in Lake Superior.
At that rate to get to the amount of water required to cover Mt. Everest would take almost 140 days of non-stop rain pouring 26,067,840 gallons per minute per square mile.
"Ahh!" you may say, "That's how it happened. God is great, and can easily cause not just 26,067,840 gallons per minute per square mile but even 27,000,000 gallons per minute per square mile!" But before you do, let's examine this for a second... We can examine it in many different ways, but for fun let's try comparing this "drizzle" to a beast of a nuclear weapon: the Tsar Bomba!
Let's pick one spot on the earth. Call it X, and put in the center of a square that's one mile by one mile. We know that rain condenses at about 2 kilometers above the surface, so let's assume that instead of individual raindrops, we have one single 27,000,000 gallon rain-drop, exactly 2 kilometers above our "X" spot. Assuming that it's spherical, our epic raindrop would be more than 188 inches in diameter, and would weigh about 217,600,000 lbs. It would take about 20 seconds to fall to earth, and would impact at approximately 200 miles per hour, with a force of approximately 1935 gigajoules – or approximately 462 tons of TNT, yielding never-before-seen destruction.
But remember, we have 196,939,900 of these drops falling down over 196,939,900 different points, for a total force impact of 381,100 petajoules per spot. The Tsar Bomba, the largest nuclear bomb detonated by the Soviets had a yield of "only" 210 petajoules, so this impact would be equivalent to approximately 1814 Tsar Bombas exploding.
And remember, this is
per minute... This bombardment would continue, minute after minute, for 140 days, releasing as much energy as detonating 365,702,400 Tsar Bombas would.

And for extra credit, let's also, assume, for the sake of argument that this was all possible and actually happened. How would this water then disappear? Let's assume it were to evaporate. At the standard, average rate of evaporation of water on our planet, the amount of water that poured down over those 140 days would take... wait for it... more than 15.6
TRILLION years to evaporate. Good thing Noah brought snacks with him!
Keep believing if you must Man of Steel, but realize, you are believing in something that's not just improbable but, arguably, impossible.