It's always fascinating to be reminded that I'm still basically ear-blind to certain linguistic patterns (the "pen/pin" merger being one I still can't even hear as different, let alone say). For a long time, I falsely assumed that because I grew up watching the same TV shows as the rest of the country, and because I didn't speak with the same accent as my family members, that I didn't have an accent at all. Turns out I do - I just can't hear it.
I took Linguistics in college and my professor could tell where people were from in the US within a couple hundred miles by their accent. Anyone who thinks they don’t have an accent absolutely does. Except maybe Nebraskans — I read somewhere that they have the most neutral, “correct” American accent, though I don’t think it was a scientific source.