Very common in Baltimore cause houses are cheaper than the rest of the east coast and so many people end up staying on for residency. The biggest hurdle, of course, is the down payment, and it really helps if your family can pony up some cash up front. A few people have set up a great arrangement where they buy a house with a room or two more than they personally need, then have their MD/PhD or MD classmates sublet. In university towns there's almost always classmates looking for a cheap ride until you move in with that special someone or move on to a different town.
Beware, however, a house is more than just an apartment you own. The costs and time for maintenance are so much more than you anticipate, so buying vs. renting is not as clear-cut of a choice as it seems (particularly as houses are no longer the equity cash-cows they used to be). I'd reccomend waiting a year or two, saving up/borrowing some cash, getting to know your new city, and waiting until a research summer when you have more time to go through all the new house hassle. I can't speak to the ease with which one can get a loan these days.
I'm sorry I can't be more specific cause I haven't done it myself, just seen many of my classmates do it, but hopefully those tidbits can get the ball rolling.
