After watching part of Prisoner of Azkaban, a particular scene in which Expelliarmus is thrown around quite a bit made me wonder what would happen if the spell was to hit someone without a wand.
Nothing or backflips (depending on the strength of the spell).
As Sparrow says, it's possible to Disarm someone using Expelliarmus, even if that person isn't holding a wand. Harry uses it to Disarm Draco of the Riddle diary.
Percy said, "As a school Prefect -", but Harry had lost his temper. He pulled out his wand and shouted, "Expelliarmus!" and just as Snape had disarmed Lockhart, so Malfoy found the diary shooting out of his hand into the air. Ron, grinning broadly, caught it.
(Chamber of Secrets, Chapter 13, The Very Secret Diary).
So, as long as the person is holding something when the spell hits them, it flies out of their hands.
There is no documented example in canon (that I'm aware of) of someone being hit by the spell whilst empty-handed. So we have no definitive proof of what might happen. Since the spell is for disarming and the person has nothing to disarm it would probably have no effect. It'd be a futile spell, like casting Stupefy on someone who's already unconscious.
That said, Expelliarmus does seem to have an innate kind of raw magical power behind it. When cast with sufficient strength it can throw a person backwards into the air. For example, when cast by multiple people at the same time at the same target it has this effect. This is seen in the books when Harry, Ron and Hermione attack Snape at the same time (this may well be the example being referenced in the question).
"Expelliarmus!" he yelled - except that his wasn't the only voice that shouted. There was a blast that made the door rattle on its hinges; Snape was lifted off his feet and slammed into the wall, then slid down it to the floor, a trickle of blood oozing from under his hair. He had been knocked out.
Harry looked around. Both Ron and Hermione had tried to disarm Snape at exactly the same moment. Snape's wand soared in a high arc and landed on the bed next to Crookshanks.
(Prisoner of Azkaban, Chapter 19, The Servant of Lord Voldemort).
So, when cast with enough force, the spell would lift someone off their feet and throw them backwards. Otherwise, it would do nothing.
Expelliarmus removes an object from the enemy's hand, so if they're not holding anything, I would assume nothing would happen. I don't know that we have an example of this in the books or movies.
However, if multiple people cast Expelliarmus against the same target, the force from the combined spells will knock the target backward. So that could be a way to fight an enemy, even if they're not armed with anything. We saw this in the Shrieking Shack in Prisoner of Azkaban, when Ron, Harry and Hermione all use Expelliarmus against Snape.
Sources and examples here: http://harrypotter.wikia.com/wiki/Disarming_Charm