Until quite recently there were only five countries that officially had nuclear weapons and were part of the Nuclear Non-proliferation Treaty (NPT). These were, and are, the US, China, France, the UK and Russia (formerly the Soviet Union.) Of these the US is by far the largest power.

Since 1974 India has also had nuclear weapons, though it has never joined the NPT. Pakistan has also had some warheads since at least 1998, and Israel is known to possess them although it still officially denies this. It is not sure how large the nuclear capacity of any of these three countries is, though you can find an estimate here.

The list may soon grow longer, as Iran and North Korea are thought to be very close to having the capability to produce their own warheads, if they haven't reached it already, and this is now a possibility with Syria too.