Wow, some of these replies are mind blowing.
@Chipper - just wow, dude. Wow.
Very early in my transition I got the occasional second glance of someone trying to "figure it out," so to speak, but no one ever said anything to me or within my earshot. I think I got a lot more "are you a boy or a girl" sort of trouble when I was in high school. (I'm closer to 40 than 30 at this point.)
I did have one moment maybe half a year pre-transition/pre-out at the office that was very *head-desk* worthy, though. We had a member of our off-site staff that I had never met before (there are lots of them) in the office on day. When we met she very excitedly said, (as if this was something they talked about), "I hope you don't mind my saying, but a number of the (other staff I work with that I haven't met) think you're a man. I told them I was pretty sure you were a woman - and here you are!" I internally winced at the time and thought, "Oh, lady, you have no idea... and that is so wrong on so many levels..."
I'm sure if/when I next see her, it will be a very interesting moment/conversation indeed.

Almost all of my really memorable "stuff strangers say" moments have been with medical professionals though, humorously (read: sadly?) enough.
I had an exceptionally curious cardiologist assistant ask me all sorts of personal questions (to be fair, I told her she could) - she was like a kid in a candy shop. She said some wholly inappropriate (and some technically racist-stereotyping) things; I'd tell the tale fully, but I can't without repeating them and I'd rather not, but honestly, she meant well. I truly believe the lady just didn't know any better. Her curiosity was genuine and she thanked me for being willing to answer all her questions - very polite otherwise.
I had one doctor send me for a mammogram, post top-surgery, with the subsequent radiologist being exceptionally nervous about telling me they couldn't do the procedure and that they weren't sure why my GP would have sent me in this instance (I figured that was going to be the case, but I gave the GP the benefit of the doubt; maybe she knew something I didn't, right?). Poor radiologist was so embarrassed by the whole thing. Felt maybe just a little bit bad to have put her in that circumstance. When she saw I wasn't angry or upset about the situation, though, she relaxed some. (I actually laughed, I couldn't help myself. As a friend so cleverly put at a later point, "Why'd she even send you, you have no mammos to gram!")
I had a dermatologist very quickly say he didn't know anything about it, upon hearing the reason for my HRT. While assessing my scalp issues and hair loss (why I was there), that the hair loss really resembled female pattern baldness much more than male pattern baldness, paused, then said, "Which I guess makes sense since the genetics don't change, only the... (starting to falter a little) appearance..." and then seemed to think he maybe said something inappropriate, and quickly moved on. I like to hope that exchange made him think a little outside his usual client box.