sure....i enter
' or 1=1 --
which creates a sql statement like
SELECT COUNT(*) FROM auth WHERE username = '' or 1=1 -- AND password ='some_md5_string'
The -- dash is sql for ignore the rest of the statement...and since 1=1 is always true it will return a count of at least 1 granting the user access to the system.
A better solution is to regex the name (ie apply a regular expression pattern ([0-9A-Z]+$) to see if the name is allowable characters (like numbers and letters only), then if it doesn't match you can kick it back the the user to try again. You can also play the same game (if you wish with the password, though it results in a slightly less strong password)
Additionally you should check to see that the row returns only 1 row, assuming that the site is coded to allow only distinct username