Mother's Day and Father's Day being around the same time as your birthday. Not a problem now, but might not be ideal birthday months for future parents. My mom deals with that, and her celebrations and whatnot tend to get merged.
As a kid, I'd say the best months are (late) May and (early) June, because school's out or almost out, and it's before most people go on vacations, and you can more easily invite friends over. Although you do have to share the months with your parents' holidays.
As an adult, I'd say (late) August and (early) September are better, because it's still warm enough for summer fun, but not scorching hot, and it's an ideal vacation period, plus no gift-giving holidays anywhere nearby to overlap.
Something I found annoying as a kid from having a b'day in Sept is that, aside from school starting making me less excited for my birthday, it was harder to send out birthday invitiations to school friends. I wouldn't see many of them over the summer, and by the time my birthday rolled around, I wasn't as close to some anymore. My birthday being earlier in the school year also meant less likelihood of new friendships having developed. So the end of the school year seems like a better time, IMO.
On another note, this is kind of funny/interesting: it seems like majority of my friends were born in either September or December, the rest dispersed randomly throughout the other months.