I just turned 30 at the end of last year. Never been married, no children. I've been in a few long relationships and am in one now. We talk about marriage, but my boyfriend is in no financial position to get married yet. It may be a couple years before he can do that. I don't even know if we'll survive, since my parents don't like him. I have, so far, spent my life studying, then training to be a physician. The vast majority of my non-physician friends are married with children. Of my physician friends, maybe half remain single, but none of them live in my state anymore. I've been feeling really down on myself for being good at many things in life, yet being a failure when it comes to finding a husband. Is it normal to be as old as I am without a husband / children?

you are normal in my opinion.
Look at it this way: You spent your 20s training for a very good career. Your 30s should be fantastic, in terms of career satisfaction -- if being a physician is really your thing, and it sure sounds as if it is -- and that's when the moolah may come rolling in, enabling you to get married and start a family.
I didn't get married till I was 28. I'm 40 now, still happily married. No kids, but that's how we like it. ;-)
I do not believe it really matters if you aren't married by 30. It's your life, live it for yourself, not for others. Don't rush things just to be like everyone else.
Now, if you are lonely, and want to meet a special person, then I'd understand. But you're only referencing a label. Being married.
Marriages don't seem to last all that long anymore anyway. Or if they do, most times people are just there so they aren't lonely. You think they are genuinely happy?
Anyway, the status quo is not where your life should be. You should live it according to your experiences. Those friends of yours will not have to put up with a guy who you say isn't financially ready, and who your family doesn't like. You will. Do you really want to settle to fit in with a group of people so you fill in the little box that says married on a form? Really?
Good luck finding the best route for you in life.
I'm a male, in my mid-30's, never been married, and have no children. I've never considered myself odd. Society may put that kind of pressure on you, especially because you're a female. But, are you really trying to impress them, or simply doing for yourself what you believe is right?
You're normal. And probably lucky as well.