If you use any sort of non-trivial algorithms handling a non-trivial amount of data, you damn well better be interested in the relationship between the runtime of the algorithm and the number of things you're asking it to handle (Big O).
If you're designing a novel algorithm (or at least, novel to you) you should at least have a passing familiarity with complexity classes. It's funny how often I hear about (or see first-hand) someone trying to figure out why their code won't always work only to have pointed out to them that their problem is NP-C.
Not only all of that, but complexity theory supplies all sorts of better algorithms—or, rather, methods to improve a general class of algorithms, I suppose—which can immediately or eventually be applied to your everyday problems.
Perhaps you don't need to deal with a lot of these problems on a daily basis, but chances are that some of the tools you use were built by people who worried about them.
It's a neat field, and I'm excited to see these advances.