While “[n]o spell yet devised enables wizards to fly unaided in human form” (QA1), various spells create flying effects.
References from the canon
- Wingardium Leviosa levitates objects (PS10).
- Dobby used a Hover Charm to float a pudding above Aunt Petunia's kitchen (CS2).
- Spells cast on broomsticks and carpets allow them to fly
- Voldemort learned to fly without a broom, much to the surprise of the Order of the Phoenix, who discovered this ability during the Battle of the Seven Potters (DH4, DH5). The only other person known to fly without a broom is Snape, who learned the magic from Voldemort (DH30).
The films show Quirrell (PS/f) and Death Eaters (OP/f, HBP/f, etc.) flying through the air. This effect, while effective visually, is definitely not canon.
Inconstistency: The book Quidditch Through the Ages was written long before Snape and Voldemort learned to fly without brooms, which is why the inconsistency about "no spell known" to let wizards fly without broomsticks.