There is. Russia, China, Israel, Europe, and the US all have anti ballistic missile programs designed to intercept nuclear missiles throughout various stages of their flight. Generally, the cost of the missiles and tracking infrastructure, and the non-100% probability to hit a given missile means they wouldn’t be able to defend against all out nuclear war, but if one, or two, or a couple nukes were launched, there’s a good chance they would be intercepted.
In the US, there is the Patriot Missile system for the launch and reentry/terminal phases of ICBM flight, and THAAD (Terminal High Altitude Area Defense) for the middle.
As far as the exact scale, the US has many hundreds, maybe thousands, of patriot interceptor missiles across, probably in the low hundreds, of launch sites all over the world. The Patriot system was mainly built for shooting down aircraft and cruise missiles, so it probably wouldn’t be very effective against ICBMs (given their speed, and the fact that most nuclear missiles contain 4-6 warheads/decoys which split up upon reentry to confuse and overwhelm air defenses). But, in the Gulf War, Patriot did supposedly intercept a high percentage (80-90+%) of slightly slower, lower altitude ballistic missiles.
For THAAD, there are only a handful of radars/launch sites across the entire world, notably: Hawaii, Guam, South Korea, Romania, Etc. THE THAAD missiles cost hundreds of millions a piece and there are probably well less than 100 total. If, say, North Korea launches two nuclear missiles and you want to make certain you intercept them, so you launch ~5 interceptors per missile, you can see how after a dozen or so missiles the system is pretty much maxed out.
Historically, the US had the Nike missile system, where people were expected to manually fly (via TV) a nuclear warhead into the incoming nuclear missile and explode it mid-air.
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