Sieve of Eratosthenes, or another prime number sieve
Depth-first search
Breadth-first search
Dijkstra's algorithm
Floyd--Warshall algorithm
Either Kruskal's or Prim's algorithm
Some implementation of topological sorting, such as by using DFS
Convex hull (I recommend the Monotone Chains algorithm)
Coordinate compression
Edmonds--Karp, or another implementation of the Ford--Fulkerson method; or a preflow-push algorithm; or, if you are preparing an ACM codebook, Dinic's algorithm. (Note: Max flow is not allowed to appear on the IOI, but may nevertheless appear on national team-selection contests)
https://www.youtube.com/results?search_query=al+sweigart+recursion