Search has always been a crucial element of AI in multiple ways. First, what many people refer to as "search" is a reflection of how what we call "intelligence" frequently involves searching something: a physical realm, a "state space" of possible solutions, a "knowledge space" where ideas/facts/concepts/etc. are related as a graph structure, etc.
Look up some old papers on computer chess, and you'll see that a lot of that involves searching a "state space". As such, search algorithms that are efficient (in terms of time complexity and/or space complexity) have always been important to making advances there. And while computer chess is just one example, the principle generalizes to many other kinds of problem solving and goal seeking activities.
Here's a reference that explains more about some of these ideas.
Note too that "search" is closely related to the idea of "heuristics" in an important way. Many search problems in the real world are far too complex to solve by exhaustive brute-force search, so humans (and AI's) resort to heuristics to narrow the state space being searched. Using heuristics can yield search algorithms that allow for reasonable solutions in a realistic time-frame, where no simple, deterministic algorithm exists to do likewise.
For some more background you might want to read up on A* search, which is a widely used algorithm with many applications - and not just in AI.
The other major regard in which something you could call "search" applies in AI is through the use of algorithms which are also often referred to as "optimisation" techniques. This would be things like Hill Climbing, Gradient Descent, Simulated Annealing and perhaps even Genetic Algorithms. These are used to maximize or minimize the values of some equation andfunction and one of the canonical uses in AI is for training neural networks using back-propagation, where you're trying to minimize the delta between the "correct" answer (from the training data) and the generated answer, so you can learn the correct weights within the network.