The algorithm commonly used for data sorting and organization is the Quicksort algorithm. Quicksort is a divide-and-conquer algorithm that works by selecting a 'pivot' element from the array and partitioning the other elements into two sub-arrays according to whether they are less than or greater than the pivot. This process is recursively applied to the sub-arrays, eventually resulting in a sorted array. Its average time complexity of O(n log n) makes it efficient for large datasets. Quicksort is widely used due to its speed and performance across various situations.