Because he was Mr. All-powerful-evil-villain-who-has-to-be-menacing. Pretty much.
He was powerful, so that's probably why...as well as it being magic, of course.
And since he was a villain, he needed to be able to do something cool, evil, and impressive :P Sure seemed to shock the good guys that he could fly!
Second, I think it was because he was so powerful. Just like Dumbledore could make himself invisible. But everyone was suprized. "Voldemort. He can-FLY."
I mean c'mon wouldn't he look ridiculous flying on a broom (actually that just gave me a funny thought)? I guess the reason he doesn't need a broom is because he'd look like an prat riding on one. XD
I think it was something new no one knew how to do, hence why McGonagall said to Harry about Snape "Looks like his Master has been teaching him some tricks."
The Order and everyone else had neevr seen someone flying without a broom before, hence the astonishment in the Seven Potters scenario.
So in answer to your question, no one knows, but I would say he did it using unknown magic.
i thi a logic answer would be 'Magic' but.. for a longest explanation, we could say that he is really powerfull, so much like to no need to ride a broomstick to fly.
and actually, you dont really need a broomstick to fly, there are many other ways.
I think it's likely that Voldemort's immense power enabled him to cast spells that normally would not be able to make a person fly, but when made more powerful, can.For instance, Dumbledore cannot become invisible just because "he's powerful and skillful," but because is able to cast a very potent Disillusionment charm. So I think Voldemort is using a combination of spells, maybe even Wingardium Leviosa, and a means of propulsion, in order to fly.
On a side note: In he books, no one (but Voldy) can fly. The movies took some liberties with apparition, I believe, for cinematic effect - i.e. oohh cool! black lights fighting evil black ones!
