Does the abbreviation for Saint in a church name require a period?
Solution 1:
I believe this is primarily a difference between American English and British/Australian English. American English usually includes the period (e.g., St. Patrick's Cathedral in New York or St. Paul, Minnesota) whereas British and Australian English typically omits it (e.g., St Paul's Cathedral in London).
Solution 2:
To expand a little on Ben's answer, the British practice is not to use a full stop where the abbreviation contains the first and last letters of the word abbreviated. So, St (which can also be an abbreviation of street) but etc. That said, British style generally tends towards minimalist punctuation.
Solution 3:
The Cambridge Guide to English Usage by Pam Peters (Cambridge University Press):
The shortened form St is normally left unstopped by British writers and editors, because (a) it's a contraction rather than an abbreviation, and (b) it contains a lower case letter. North Americans when using a saint's name usually punctuate it as St., as exemplified in the Chicago Manual (2003): and this style is carried over into placenames (e.g. St. Louis) in encyclopedic dictionaries such as Random House (1987) and Canadian Oxford Dictionary (1998).