Radix sort
Radix sort sorts keys digit by digit (or byte by byte), usually least-significant digit first (LSD), with a stable pass such as counting sort on each digit.
For $n$ keys of $d$ digits in base $r$, time is $O(d(n + r))$. Fixed-width integers and strings with bounded length are the sweet spot. It is not a comparison sort.
MSD radix sort can short-circuit on prefixes and is closer to trie / string algorithms. For general Comparable objects, stick to comparison sorts.