Corrosion rate of various metals in salt water

If I took a cast iron skillet with no coating and dropped it in the ocean, how long would it take before it would be absolutely destroyed?

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Unprotected wrought iron loses an average of about 1mm per year to corrosion in sea water, and can therefore sit on the ocean floor for decades.
In the absence of oxygen, it becomes infused with salts and other minerals and covered with surface encrustations - sand, sediment, marine life, and iron oxides and chlorides. The danger occurs in removing it from the water - as soon as it hits the air, the minerals in it start to dry and crystalise and can split the metal apart, much like water does to wood when it freezes.

Also what sort of specific metals or alloys are commonly used for things that are always underwater, like bridge cables and beams, submarine hulls, etc?

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Submarine hulls are often built from titanium, which is 45% lighter than steel and highly resistant to corrosion. Steel hulls, decks etc are coated with antioxidising paint but have to be constantly refurbished and repainted.

I know I'm generalising here, but marine hull construction and corrosion prevention is a massively complicated subject!

I'll see if I can help a bit here:

Iron ore: From a chemist's point of view, this is not a metal but a salt. To a layman, it's a rock. There are several sorts of iron ores. The most commonly used ones are magnetite and hematite. Both are iron oxides, basically the same as rust already. There are a few oddballs like pyrite (fool's gold), too. Unless you have a very strange iron ore, it won't disolve in water. If you want a lengthy list of iron ores, follow this link:

http://www.minerals.net/mineral/sort-met.hod/affili/fe-ores.htm

I'll list the metals in the order that they corrode fastest:

Fastest rusting: Cast Iron, Steel (more or less equal other than stainless and the like)
Chrome plated steel
Bronze and Brass
Stainless Steel
Slowest rusting: Titanium

The usual ways to deal with metals that are kept in salt water is to use a combination of paint and zinc anodes. If you put a piece of steel and a piece of zinc in contact with each other underwater, the zinc will rust away before the steel rusts. Replacing the zinc before it can completely disolve into the water keeps the steel from rusting.

XThe NavigatorX said:

Thanks. I didn't realize that removing it from the water was more dangerous than leaving it in. That's important.

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This is why some shipwreck recoveries are so controversial -- such as raising The Titanic. Unless you have a plan to prevent the damage caused by this oxidization, it's best to leave the ship where it is in the water.

On a side note -- not only metal ships are at risk in recovery. There are some wooden ships wonderfully preserved for ages in "dead" (i.e. no oxygen) water that can be destroyed if raised to the surface.