Genetic algorithms have the ability to capture the imagination of public and computer science students because they can find very messy and random solutions if you run them long enough.
In the general context of search and optimization algorithms they are not impressive. When you can't use anting better, like Mote Carlo or simulated annealing, evolutionary algorithms are often the last hope before brute forcing it. GA can be very impressive when you can restrict the search space and find good representation for the problem.