The suffix -ize has been in common use since the late 16th century; it is one of the most productive suffixes in the language, and scores of words ending in -ize are in daily use.
Some words ending in -ize have been widely disapproved in recent years, particularly finalize (first attested in the early 1920s) and prioritize (around 1970). Such words are most often criticized when they become, as did these two, vogue terms, suddenly heard and seen everywhere, especially in the context of advertising, commerce, education, or government—forces claimed by some to have a corrupting influence upon the language. The criticism has fairly effectively suppressed the use of finalize and prioritize in belletristic writing, but the words are fully standard and occur regularly in all varieties of speech and writing, especially the more formal types.
The British spelling, -ise, is becoming less common in British English, especially in technical or formal writing, chiefly because some influential British publishers advocate or have adopted the American form -ize.