Huffman coding
Also known as: Huffman code, Huffman tree
Huffman coding builds an optimal prefix-free binary code for known symbol frequencies: repeatedly merge the two lightest trees, using a priority queue / heap. It is the standard greedy example in algorithms courses.
The resulting code tree assigns short bitstrings to frequent symbols. Optimality is among prefix codes for those frequencies; it is not magic compression for arbitrary files without a frequency model.
Time $O(n \log n)$ for $n$ symbols with a binary heap. Related ideas show up in JPEG-style pipelines and in teaching priority queues.