Automata theory may seem arcane, but if you want to truly understand concurrent programming, protocol design, robust systems, etc, you need good cognitive models. Heck, Erlang (one of my favorite languages for massively distributed computing) has some nice OTP stuff (http://www.erlang.org/documentation/doc-4.8.2/doc/design_pri...) built in for using FSMs to make your code sane and robust.
FSM's are one of the theoretical CS concepts that it is easiest to see the practical use for, but other TCS tends to be just as useful if you look at it right. Eg, space complexity right? For the most part that doesn't matter, does it? Nope. A bunch of modern internet-sized problems end up being streaming problems (http://geomblog.blogspot.com/2005/05/streaming-algorithms.ht...), and you need to understand basic space complexity, linear algebra, and probability, all of which a good CS degree will get into your head. I think the role of a good CS degree is to get some theory into people's heads, so that they have the right cognitive models for tackling difficult problems that come up in the real world.
I'm not saying that a CS degree is necessary to be a good programmer, or that you can't pick up those mental tools without a CS degree if you need them. But, it is easiest for most people to learn that kind of stuff in a university environment. I for one didn't know that I needed theory to work on the sorts of massive-data problems I was interested in, before going to university. A good CS degree knows about your unknown unknowns.