technically the dress code at my work is on the nice side of buisness casual, slacks and button-ups or collared shirts, no logos or slogans that aren't associated with work, so-on.
However the enforcement of dress codes (and importance of dress in general) seems to (for my industry, anyway) seem to relate with distance to DC. So what we actually wear are jeans for most everyone (some of the upper management I deal with wear slacks) and polos, though I've seen my boss's boss regularly wear t-shirts on non-Fridays.
Anytime someone travels back east though you gotta pack your clothes to the audience. Going to PAX? Probalby just need slacks, blazer and nice shirt. Going to DC? Pack the 3-piece.
As for how important it is... eh. We mix with military a lot. Currently sharing my cube farm (8 cubes in the room) with an airman. We also have a lot of retired military. And the younger ones haven't shaken the military-dress habit yet. One of the other guys in my cube farm, I kid you not, uses a brush and occasionally spot wax on his shoes multiple times a day. Point being that when an admiral walks in (and I have had days where an admiral just popped by) you don't want to be caught looking like a dumb civvie.
But most days I go around in jeans, a nice shirt (I like nice shirts) and my vibram five-fingers. And occasionally a super-hero vest. It's not technically per dress code, but few people in my building stick to the technical dress code.