I just finished my second year in medical school. I've consistently kept $1500 in savings plus a $1500 cushion in my checking account. My husband and I also have $7500 in mutual funds that we haven't touched since we started school (he's in grad, I'm in med). It hasn't hurt us regarding federal loans, because our total annual income up to this point has been a *grand* $15,000 (from my husband's graduate student stipend), and so we're eligible for the full $38,500.
Before school started, we had a financial advisor tell us that from a monetary perspective (i.e., not having to take out as many loans), it'd probably be best to cash out the mutual funds. However, because it was a gift from my husband's grandfather, and not from our own income, and because it provides a basis for future savings (and at this point we can't increase our savings at all because we have no significant income), we decided to not cash it out. Essentially, it is a good cushion for us, and it makes me feel like we're not totally behind in starting to save for our future.
Also, the amount in savings has saved us more than once. We actually had our debit card number stolen, and somebody cleaned out our checking account. The bank gave us the money back--but it took them over two weeks to do so, and we had NYC rent and groceries to pay. So the emergency savings IS a very good idea, in my opinion.
However, if you have credit card debt, I would suggest using savings to pay that off, as well. You DON'T want to carry that into school, as you can only lose money that way.
Good luck!