Well here you have some of the greatest rockets ever made. Both are ABM missiles, meaning they are to prevent a nuclear IRV from hitting a target. For this reason, and also because they were the low altitude, terminal defense part of the ABM system, they had to be really really fast.
This is the sprint system. It was a two stage rocket with a 1 KT Neutron bomb to take out the IRVs via explosive force and neutron flux. It worked up to 100,000 feet, and could hit more than mach 10. It was about 7,700 lbs, but took off with 650,000 lbs of thrust. Acceleration was 100 Gs.
Here is a test flight of the system. It was ejected from an underground silo by compressed gas and a sabot. The nose cone had to radiate incredible amounts of heat: up to 6200 deg F from the frictional heating. Flight time was 15 sec, or less.
As if the sprint wasn’t crazy enough, there is this little guy. HIBEX, possibly the single most insane rocket ever. It was supposed to target nuclear devices at under 20,000 feet altitude. Now keep in mind, these devices would then be falling towards the target at about mach ten.
Not as much info is out about this rocket, but it appears to have accelerated at 400 gs, which is just incredible. And it was only 17 ft tall! Flight time was 2 sec., and mach 8 was had after burnout in just 1 sec.