My edition of Fowler (Modern English Usage) gives a full explanation. The other posters are correct in that the OUP and the Times (for example) prefer -ize; but Fowler also gives a list of common words where -ise MUST be used:
advertise, chastise, circumcise, comprise, compromise, demise, despise, devise, disguise, enterprise, franchise, enterprise, exercise, improvise, promise, supervise and surprise (there are others but these are the most commonly used).