PageRank (search ranking), A* algorithm (pathfinding), simplex (linear optimization), branch prediction (in CPUs), autocomplete

There is also a large set of algorithms for adversarial search problems, such as playing board games, that traditionally don't use machine learning. Minimax is the simplest one, and then there are negamax, alpha-beta pruning, negascout, etc. I believe Stockfish (the world's strongest chess program, or close to it) has actually improved its evaluation function using machine learning, but this is a fairly recent development.

Any form of constraint solving tech. SAT solvers (used in hardware-synthesis, software verification, math proofs, etc.), Mixed Integer Solvers (usually sold for tens of thousands of dollars) that are used for hardcore optimization problems, Google's Operations Research toolkit (OR-tools), etc.

Unlike most algorithms, these things are general purpose, they can solve any* NP-complete problem (*usually in a useful amount of time).

My manager refers to these things as "Machine Reasoning" in contrast with "Machine Learning", since they start from the rules instead of from examples.

If you've used a GPS navigator you've used AI, Pathfinding is a type of AI. Saw mills use planning algorithms to extract the maximum amount of useful planks from lumber, that's AI.

The most popular text book in the subject might be a good starting place: https://aima.cs.berkeley.edu/

No personal experience here, but my understanding is that expert systems were considered a type of AI and were in the early days mostly implemented as a collection of "if-then" statements.