Nuclear weapons exist because at one time, we felt that they may become an important strategic weapon that would give us leverage over our enemies. However, that secret got out and the Russians were the next to acquire "the bomb." From here, it filtered down into many nations such as Iran, India, Pakistan, North Korea, France, England, Israel, etc.
Now, the only reason to have a nuclear weapon is so the other guy with a nuclear weapon won't attack you. It is one of those things that we all wish everyone would get together and say "We do not need them anymore. Let's all agree to dismantle them and never build another." However, this will never happen, so we have them on the MAD principle: Mutually Assured Destruction. This means that if you launch one, I'll launch one, then you'll launch more, and I'll launch more, and we'll both be obliterated.