It really depends. If you can find an older, relaxed, well trained dog and make the dog a serious priority, it should be fine. It'll be tough at times during basic sciences, and it'll be tough/impossible during clinical years if you're living alone. Due to travelling and long days, you will need someone to take care of it during externships as was mentioned. Some 3rd year local rotations will also have hours too long to really be fair to the dog also. From what I've seen, even leaving early for child care issues doesn't fly very well with most attendings since you are skipping work other students/residents must make up for, so something tells me that "I have to take off a couple hours early to let out my dog" really wouldn't go over too well.
If you're single and in an apartment, a cat or fish would really be better options IMO. Most students live in places that are pretty small and close to other animals and people, so barking can be a problem. If you get a small dog, that would solve the apt size problem somewhat, but many small dogs are yappy with small bladders. If you get a medium or big dog, it will probably be able to "hold it" longer, but then the dog probably won't have as much room as it needs. You will have some long days studying where you pull all-nighters or are at school dawn til dusk going to class and reading, so the dog might get pretty bored or a stressed bladder.
My fiancee and I have a medium-sized dog and do fine, but many days one of us needs to go out of our way to stop by her condo and let it out. If it were just me having to rush home after class/clinic every day, I don't think it'd work out. Either that, or the dog would barely ever get the attention it needs because I'd be coming home dead tired to take it on a quick walk so I could go to sleep or back to studying. I'd say the dog does pretty good between both of us letting it out and excercising it, but it'll be a lot better once I start residency and we get a house with a fenced in backyard where it has more room.
If you are single and do decide that you can handle a dog, I'd definitely recommend avoiding a puppy or very active dog (<2y or so depending on breed). They need to be excercised and "go" more often, it takes significant time to train, and they are just too active to leave home alone for 8+ hours without coming home to chewed up shoes/garbage/etc or neighbor complaining of barking. That's not even to mention that puppies cost a lot in vet bills, and most students are already on a pretty limited budget.
Here's a thread I saw on this topic a lil while ago...
http://forums.studentdoctor.net/showthread.php?t=433887
