The Lockheed F-104 Starfighter was (as far as I know) the first aircraft that had so much power, it could accelerate straight up in a vertical climb (provided it wasn't burdened by too many external stores). Its climb rate was almost as good as the much later, much more powerful F-15 Eagle. It held numerous time-to-height world records.
It was also extremely fast, thanks to its pencil-like fuselage and razor-thin wings. Here it is in a very low pass.
For a fast jet, that's haircut distance from the ground!