In consideration of @jszbody post, you should also update your password field to tell you want scheme you're using.
Where you have an MD5 hash now, you might have just "BAC232BC1334DE" or something.
When you go to SHA or whatever, you should change it to: "SHA:YOURSHAHASHHERE".
Because you can't change any of your existing passwords right now. This will make it more backward compatible, since now you can support both schemes.
Since you get the original password during login, you can dynamically upgrade your passwords in place as people login.
You get your user record, check the password. If there is no scheme, use MD5, and compare passwords. If they're correct (i.e. they can log in), you can update their old MD5 password to the new SHA password.
Also, it seems you are not salting your passwords. You must salt your passwords so that when Mary Sue uses "ilovekittens" for her password, and Big Jake Mahoney uses "ilovekittens" as his password, you don't get the same has for identical passwords.
You can store the salt in the password as well: "SHA:RANDOMSALTCHARACTERS:YOURSALTEDHASHHERE".
Salting is highly recommended. Unsalted, it pretty much doesn't matter a whole lot what scheme you use.