Israel has nuclear weapons (created during the time Israel collaborated with the French, with mutual assistance regarding nuclear programs), but official sources will neither confirm nor deny the existence of such weapons when asked. Even then, France eventually did impose an embargo against Israel, at which point the Israelis turned to South Africa (during The Apartheid Era, mind you) to complete the project, jointly developing their nuclear arsenal with South African collaboration. The Vela Incident, in which an American satellite detected what may well have been a nuclear explosion in the southwestern Indian Ocean, is suspected to have been a joint Israeli-South African nuclear test. Politics indeed do make for strange bedfellows. South Africa eventually dismantled their nuclear arsenal, becoming the first, and thus far only nation to voluntarily exit the Nuclear Club. note Israel...didn't.
Any speculation you may hear about quality and quantity of such weapons is likely just that—speculation, although Israeli officials have on several occasions openly admitted to it before retracting the statement. But the fact that Israel has at least one nuclear weapon in its arsenal is sometimes called "the worst-kept secret in the Middle East". According to historians and biographers of Israeli figureheads, this is completely intentional—as Doctor Strangelove will tell you, the nuclear arsenal's purpose is to deter, not to be used. When Mordechai Vanunu, an Israeli nuclear technician, disclosed details of his nation's nuclear arsenal to the London Times in 1986, he was imprisoned for treason.
The most terrifying aspect of the Israeli nuclear program is the concept of "The Samson Option". The Samson Option is the name that some military analysts have given to Israel's hypothetical deterrence strategy of massive retaliation with nuclear weapons as a "last resort" against its enemies, which may not be limited to those nations actually attacking. The name refers to the biblical Samson's last words: "Let me die with my enemies!"* Again, as with anything regarding this subject, Israel has never officially confirmed or denied this - no sense in discussing the usage of a weapon you don't have. This strategic ambiguity serves multiple purposes: it solidifies the Israeli bargaining threat of "help me out or you will suffer" to a larger power that would rather stay out of it by staying neutral via internationally removing (some) control over their own nuclear retaliation response, while not explicitly targeting anyone in particular and garnering resentment with bad PR. The big assumption with this and any nuclear strategy involving mutually assured destruction is that your opponent isn't a Death Seeker who hates you so much that they also don't care if they die so long as you do as well.