Sorting and Searching
When it comes to algorithms that programmers know and love, the stereotypical examples are often algorithms that either sort or search through a given container of elements. For the most part, sorting and searching methods are two sides to the same coin and are almost always described together due to their similarities. To be honest, they are also good thought exercises for new programmers. It's often inspiring to hear how individuals who have no programming experience go about solving the problem, because there are so many ways to do it!
All said, sorting and searching are fundamental to numerous algorithms and really show how computer science has evolved with time to lower the complexity of problems that seem straightforward at first-glance.
As the Archive evolves, more and more sorting algorithms will be added, so feel free to let me know your favorite algorithm and I'll do my best to put it in! Right now, there are only a few (straightforward) examples, so expect some more complicated algorithms in the future!