The Fast Fourier Transform (1965) is one very important algorithm that comes to mind, speeding up Fourier Transforms from O(N^2) to O(N log N). Quicksort (published 1961) might be another example, but since sorts in the 1950s usually ran on tape drives, it's hard to compare.
On the whole, computers of the 1950s were extremely memory-limited, so many modern algorithms aren't entirely relevant. For example, the IBM 7090 (1959) was a large-scale scientific computer and had an address space of 32K words. As for performance, it did 39,500 multiplications per second. A modern supercomputer is trillions of times faster; that makes up for a lot of bad algorithms.
Most modern problems are going to have a hard time fitting in a 1950s computer, regardless of the algorithm. On the whole, I think you'd be better off with 1950s algorithms on a modern computer than vice versa. On the other hand, modern cryptographic algorithms on old hardware would be infinitely better than old algorithms on modern hardware.