I don't think you need to worry about the relationship status quo for med students/doctors as much as you need to concentrate on what is right for you. This goes for anyone in a relationship. People define their relationships in all sorts of ways, so I don't think there can be a standard. It doesn't matter how many other people have successful long distance relationships; if it makes you miserable, it's not worth it. However, if you are so happy with your SO that distance doesn't matter, you may find that being in a LD relationship isn't as bad as you expect, and you choose to stay "together." What's most important is that your situation works for you (and your SO), so stay true to what you want, communicate with your SO about what he/she wants, and acknowledge that some things may be beyond your control. If you are both on the same page and willing to make some compromises (NOT sacrifices-- it's an important distinction) then you should be able to be reasonably happy with whatever you decide, even if the situation is less than ideal. If you cant maintain a relationship in a way that works for both you and your SO, then its ultimately not the right relationship for you.
Another thing to consider is that medical school is difficult and time consuming. Again, this could work both ways: If you spend 90% of your waking hours at school studying, living with your SO may be the only way you get to spend any time with them. However, if you have to be apart, you know you wouldn't otherwise be spending all your time together, so you can concentrate on making the visits really meaningful. Think about both of these situations in relationship to you and your SO. Is one of them obviously more indicative of how you operate? If so, then its probably the right choice for you; if not, then maybe this decision isnt as ultimate as you first thought.
I know that in my case, being in a good relationship has helped me be able to work hard and accomplish what I have. My SO is not a med/pre-med, but he is equally dedicated to his career (music), which is quite possibly even harder to succeed in than medicine. The differences in our lives give us the ability to support each other when we need it because we are NOT going through the same things. When I get stressed, it doesn't transfer to him, so he can be there for me 100%. When he gets stressed, I am likewise detached from his situation enough to be there 100% for him. While he may not understand first hand the things I am doing, he understands their importance to me, and when we spend time together it is a much-appreciated break from medicine. Plus, I know that if I can explain the things I am learning to someone with no background in science, I must have a good grasp on what I am saying!
As for schools, I am lucky enough to have choices in where to go to medical school, and I am choosing to stay with my SO even though my 2 top choice schools are in other cities. I know that the school I will most likely be attending is still an excellent place where I will be able to get a good education, and I believe that I will be a better med student with my support system intact. If I had been making this decision at 22 when I graduated from college, I know I would have chosen differently, but then again, I would not have the choices that I do if it hadn't been for my SO. His emotional support has been key to my success as a post-bac, and the difference in my collegiate vs. post-bac record reflects this. So for me, this is an easy compromise to make (although I have still spent many hours contemplating it!): I know I will be happier living with my SO, and this will be a huge benefit during my medical education. And I am making this decision knowing that if I had chosen otherwise, my SO was willing to make the best of a difficult situation and stick out a LDR because he values our relationship so highly. If he hadn't been willing to make that more difficult compromise, I might have chosen to attend school in a different city since I wouldn't have felt as confident in my relationship. As it is, I know that I am not sacrificing anything by staying: I get to live with a man who feels as strongly about me as I do about him, and I will attend an excellent med school (even though it wasn't my top choice).