Many people in the UK believe that words ending in “-ize” such as “organize” are US spellings, and that the correct spelling is “organise”. However, the Oxford University Press insists that words such as computerize, capitalize, capsize, organize, organization, privatize, publicize, realize should take the -ize ending, but that others, eg analyse, advertise, advise, arise, compromise, disguise, despise, enterprise, exercise, merchandise, revise, supervise, surprise should take the -ise ending.
In the Concise Oxford Dictionary you will often find that both options are possible in British English - 'realise' or 'realize', 'organise' or 'organize' - whilst for other entries -ize is listed as unmistakably American, e.g. 'analyse' = British English, 'analyze' = American English.
Even I get confused, but I tend to veer towards the -ise ending.
Here's a checklist you can use:
Noun and verb: Where the noun and verb are the same (like “exercise”), use -ise.
Pronounciation: Anything that doesn't sound like “-eyes” uses -ise, such as “promise”.
Stem: Where the stem word (usually Latin or Greek) ends in “is”, then use -ise, as in vis (to see) gives “televise”.
Anything else: Use -ize.