Are there some non-agglutinating languages that have vowel harmony?

Originally Answered:

Are there any fusional languages affected by vowel harmony?

Not necessarily the answer you were looking for, but the Greek dialects of southern Cappadocia (e.g. UlagaƧ), which were the most profoundly influenced by Turkish, had vowel harmony extending to verbal inflections. See Richard McGillavray Dawkins’ Modern Greek in Asia Minor.