Analyse is the "correct" spelling that we're taught in school, but there has been a gradual shift towards American English due to the dominance that Americans have over the media (e.g. "math" instead of "maths"). Analyse/analyze is one of those words that is in transition, and I suspect we'll be using the American spelling in 50 years' time.
In a professional context I've completely abandoned British English. Anything informal I still use it but for writing code and communications it seems more polite especially for people who speak English as a second language.
As much as would have liked it to be the reverse think it's fair to say that American English is now completely dominant worldwide and that will only continue.
