The current total is 71 active and 2 reserve as of May 2011 -
Commissioned
14 SSBN's (Ballistic Missile Submarines)
4 SSGN's (Cruise Missile Submarines, converted SSBN's)
53 SSN's (Fast-Attack Submarines)
Reserve
2 SSN's (688-class Fast-Attacks)
The USS California, the newest Virginia-class SSN, is scheduled for commissioning in October 2011, with another 4 on the way.
The US, Russia, Great Britain, France, China and (recently) India have nuclear submarines.
The PLA navy has more than 225,000 personnel and is thought to have as many as 70 submarines, 10 of them nuclear-powered
USA has the most nuclear submarines
Nuclear power plants are very large fixed installations on land. There are many reactors however in the US navy ships and submarines
230
170
nearly 155
Argentina had diesel-electric submarines while the British had nuclear-powered submarines.
Reactors power submarines and many surface ships. Nuclear weapons.
A number of nuclear submarines sank, and the circumstances vary from accident to accident. Wikipedia has a list, and by going there and entering "List of sunken nuclear submarines" you can review that list.
Nuclear submarines are powered by a nuclear reactor and they are completely independent of air, so there is no need to surface frequently.
Most submarines now have a single nuclear reactor. Some smaller, coastal submarines have a single diesel.