The Silent Hunter series is largely accepted as the pinnacle of submarine simulation. The PC and console games are pretty much the best way to feel like you're in charge of a real old-school submarine. Ubisoft currently owns the license, and they've now released an iPhone version of the brand, which has you piloting a German U-boat around the North Sea in 1939. It lacks most of the depth (pun intended, sorry) that Silent Hunter is known for; the game is basically a shooting gallery, and while there is a bit of strategy in ship placement, the plan is mostly to kill the other side before they kill you.
Still, it's fun, and except for a little bit of lag in the controls, it plays pretty well. You can send your sub up or down in the water (make sure to stay below when you get close to the escort you're stalking) and fire torpedos at any targets you spot. The game's campaign mode has 12 different missions, and each one offers up a nice set of progressions, from just hunting down merchant ships to taking on destroyers, on up into anti-air combat. You can earn XP to upgrade your sub and its parts, but the gameplay doesn't change much; you pretty much just navigate to the right spot, and then open fire at the right time.
The graphics are presentable on the iPhone, but the music is actually excellent. All in all, the game is definitely worth a go at US $1.99 (which is what it's on sale for in the App Store right now). You won't find anywhere near the level of complicated and subtle gameplay that the larger versions of Silent Hunter have, but if you just want to line up a destroyer in your sights and yell, "Torpedo away!", Silent Hunter Mobile does the trick.