Has a submarine ever gone under the north pole?

Absolutely; the first boat to do so was the USS Nautilus (SSN-571) on her historic trip under the Pole in August 1958. In the past 35 years, regular visits by submarines (known as ICEX's, or Ice Expeditions) to the North Pole happen every year, usually supported by the Applied Physics Laboratory Ice Station (APLIS).

Having been there myself, the Arctic is a completely different world, both on the ice surface and underneath. Sonar-wise, it's extremely noisy, due to the ice floes constantly shifting and cracking with the water movement and storm activity on the surface. This makes for a perfect hiding area for Ballistic Missile submarines, and is a large reason why Arctic submarine activity has increased significantly during and since the Cold War.

Have a look at my Supervisor Bio page for some pics I took during LANTSUBICEX '86.