The immediate reaction I tend to get is surprise. Which is... well, surprising. Shakespeare is so well-known and so often quoted, I just kind of figured more people liked him. Apparently not. A lot of students I mention this to say, "But he's so hard to understand." Maybe I've been in school to long but I'd rather read everything Shakespeare has ever written than try to tackle David Hume or Descartes again, thanks. Shakespeare's writing is different than what we're used to, I suppose, but I find it fairly easy to get used to the way he writes. Also, his style allows for some of the best insults I've ever heard, which is certainly a plus.
I also worry, because I am a bit of a hipster and am used to such things, that people will assume I'm saying that just to sound smart or be "fashionable." It's not something I should really be concerned about, but there is a certain elitism sometimes associated with Shakespeare. Which is kind of strange, really, because they're the sort of plays done by all sorts of theater groups, from high schools to world renown organizations. George Dawson has a pretty nice quote on this issue:
So yes, I am a Shakespeare fangirl. I don't assume everyone else is, but I love being one. Though I warn you, if you mention Richard III or Iago or Henry V around me, be prepared to have your ear talked off about my extreme appreciation for them. :)