There is not enough information in the books.
Specifically, I would like to disagree with some of the lines of argument in the other answers:
The quote of Percy showing them the doors to the stairs leading to the dormitories demonstrates that all the same-gender students in the year shared the same dormitory.
I do not believe this necessarily indicates this. It seems fairly clear that the doors in the common room didn't lead directly to the specific dormitories; rather the doors in the common room led to the respective areas for all the boys dormitories and all the girls dormitories. Consider that in Chamber of Secrets when Harry enters his dormitory for the first time, it is described as the same dormitory from the previous year and it is behind another door:
They hurried up it, right to the top, and at last reached the door of their old dormitory, which now had a sign on it saying SECOND YEARS.
It sounds like the staircase branches off to various doors that lead to the different dormitories.
Additionally, in Order of the Phoenix when Ron runs up the staircase to Hermione's dormitory and it turns into a slide, two fourth year girls come sliding down:
He was on the sixth stair when it happened. There was a loud, wailing, klaxonlike sound and the steps melted together to make a long, smooth stone slide. There was a brief moment when Ron tried to keep running, arms working madly like windmills, then he toppled over backward and shot down the newly created slide, coming to rest on his back at Harry's feet.
"Er — I don’t think we’re allowed in the girls’ dormitories," said Harry, pulling Ron to his feet and trying not to laugh.
Two fourth-year girls came zooming gleefully down the stone slide.
"Oooh, who tried to get upstairs?" they giggled happily, leaping to their feet and ogling Harry.
This shows that the fourth-year dormitory was up the same staircase as Hermione's dormitory. Indeed immediately before this, the door is described as the door that leads to the girls' dormitories (i.e. plural):
"I wonder if Hermione's seen this yet?" Harry said, looking around at the door to the girls' dormitories.
Percy leading the first-years out of the Great Hall implies that it was all of the first-years.
I think that this is also not necessarily true. It is possible that other prefects were leading other first-years. There are, after all, six prefects in the house; it would be odd for only one prefect to be leading all the first years. Indeed, in Order of the Phoenix when Hermione and Ron are prefects we find that both of them lead the first-years from the Great Hall:
Hermione jumped up, looking flustered.
"Ron, we’re supposed to show the first years where to go!"
"Oh yeah," said Ron, who had obviously forgotten. "Hey — hey you lot! Midgets!"
"Well, they are, they’re titchy..."
"I know, but you can’t call them midgets... First years!" Hermione called commandingly along the table. "This way, please!"
Similarly,in Philosopher's Stone when there was a troll on the loose and the students were sent back to their dormitories, Percy is the only prefect mentioned as leading students, yet it would be strange to assume that Percy was the only prefect doing this when Dumbledore announced to the prefects in general to lead the students back:
"Prefects," he rumbled, "lead your Houses back to the dormitories immediately!"
Percy was in his element.
Follow me! Stick together, first years! No need to fear the troll if you follow my orders! Stay close behind me, now. Make way, first years coming through! Excuse me, I'm a prefect!"
Are we to assume that all the other prefects simply ignored an explicit directive from Dumbledore? It is more likely that the other prefects were also leading students and they simply weren't mentioned because it was not important to the story (indeed, we don't even know who the other prefects were).
In fact, in neither of the above cases is there any mention of Percy making sure that all the first years are with him. If all the first years were supposed to be following him you might expect him to check that he actually has everyone, particularly when there was a troll on the loose. If, however, there were multiple prefects leading first years, it would make perfect sense for him not to check — he obviously wouldn't have all the students as some of them would be following other prefects. Indeed, when Harry and Ron break away from the group to go rescue Hermione, we don't ever find that Percy noticed that two students were missing.
Now if we assume that there could theoretically have been other dormitories behind the door that Percy showed them, and other first year students besides the ones that Percy led, the next question would be how many Gryffindor girls there were in Harry's year.
As mentioned in the other answers, we know there are at least three: Hermione, Lavender, and Parvati. However, I think it is very likely that there were others as well, perhaps even a whole bunch.
Consider that in my answer to how many boys there were in Harry's year, I pointed out that we need to account for 30 students in the fifth year Defense Against the Dark Arts class and more than 130 students in the house as a whole. Much as I argued there that it would be very unlikely for all the unnamed students to be girls or in other years, it would also be unlikely for all the unnamed students to be boys or in other years.
So there may have been multiple girls dormitories for Harry's year. And we also don't know that there are specifically five beds per dormitory (that may just be Harry's), so Hermione could have an unknown number of roommates chosen from an unknown number of unnamed characters. We can't even assume that she shared a dormitory with Lavender and Parvati, because if there really are additional girls and other dormitories it is possible that Lavender and Parvati slept elsewhere.
Arguably, not Parvati or Lavender.
There is perhaps evidence that Parvati did not share a dormitory with Hermione. When the students are leaving the common room to go to the Yule Ball, we find the following exchange:
"Right," said Ron, looking around. "Where's Hermione?"
Parvati shrugged. "Shall we go down then, Harry?"
If we assume that Hermione had been getting ready in her dormitory and she shared a dormitory with Parvati, Parvati probably would have seen her there even if Hermione finished getting ready and left before her. Thus, we might expect Parvati to have responded to Ron with something like "she was getting ready with us in the dormitory, but she left already" rather than simply shrugging.
We also know from Half-Blood Prince that Parvati and Lavender were best friends:
When they left the Gryffindor table five minutes later to head down to the Quidditch pitch, they passed Lavender Brown and Parvati Patil. Remembering what Hermione had said about the Patil twins' parents wanting them to leave Hogwarts, Harry was unsurprised to see that the two best friends were whispering together, looking distressed.
While certainly not proof, the fact that they were best friends would certainly make sense if they were roommates. If Parvati and Lavender were roommates, and Parvati and Hermione were not roommates, then Lavender and Hermione would not have been roommates. Additionally we never really see Hermione having any sort of friendship with either Parvati or Lavender, which would also be better explained by assuming they roomed separately.
Further circumstantial evidence that would support Hermione not sharing a room with Parvati or Lavender comes from how they talk about her. When Harry asks Parvati if she knows any girl that Ron could go to the Yule Ball with, we see the following:
"What about Hermione Granger?" said Parvati.
"She's going with someone else."
Parvati looked astonished.
"Ooooh — who? she said keenly.
"No idea," he said.
Referring to Hermione by her full name makes it sound like she is not so familiar with Hermione, or that she does not expect Harry to be so familiar with her. But if they were roommates, Parvati would presumably have been familiar enough with her to refer to her simply as "Hermione" and she probably would have known that Harry was good friends enough with Hermione to understand the reference.1 Additionally, Parvati apparently had no idea that Hermione had a date. While it is certainly possible, even probable, that Hermione would not have told her roommates who her date was, this makes it sound like Parvati and Hermione had never discussed it at all. But one can easily imagine that the subject of dates would have come up in the girls dormitory at least once, so unless Hermione had outright lied and said she didn't have a date, you might expect her roommates to know that she had one.
Lavender, too, refers to Hermione by her full name when mentioning her to Harry in Half-Blood Prince, again perhaps implying a certain unfamiliarity that you might not expect if they were roommates:
"Is Hermione Granger still visiting him?" Lavender demanded suddenly.
Yet a further instance that would be better explained if they were not roommates comes from the following scene in Half-Blood Prince:
"Hi, Parvati!" said Hermione, ignoring Ron and Lavender completely. "Are you going to Slughorn's party tonight?"
"No invite," said Parvati gloomily. "I'd love to go, though, it sounds like
it's going to be really good... You're going, aren't you?"
"Yes, I'm meeting Cormac at eight, and we're —"
There was a noise like a plunger being withdrawn from a blocked sink,
and Ron surfaced. Hermione acted as though she had not seen or heard
"— we're going up to the party together."
"Cormac?" said Parvati. "Cormac McLaggen, you mean?"
"That's right," said Hermione sweetly. "The one who almost" — she put a great deal of emphasis on the word — "became Gryffindor Keeper."
"Are you going out with him, then?" asked Parvati, wide-eyed.
"Oh — yes — didn't you know?" said Harmione, with a most un-Hermioneish giggle.
"No!" said Parvati, looking positively agog at this piece of gossip. "Wow, you like your Quidditch players, don't you? First Krum, then McLaggen."
"I like really good Quidditch players," Hermione corrected her, still
smiling. "Well, see you... Got to go and get ready for the party...."
She left. At once Lavender and Parvati put their heads together to discuss
this new development, with everything they had ever heard about
McLaggen, and all they had ever guessed about Hermione. Ron looked
strangely blank and said nothing. Harry was left to ponder in silence the
depths to which girls would sink to get revenge.
Here again, they seem to relate to each other in a way that implies that they do not spend every night in the same room. Hermione's "didn't you know" in particular seems indicative of this. Remember, Hermione has not actually been going out with Cormac; she is simply trying to get back at Ron. If Hermione and Parvati were roommates, Hermione's exclamation would be much less believable. If she truly had been going out with Cormac and she shared a room with Parvati then Parvati could have simply responded with something like "of course I didn't know; you never once mentioned it in all the times in the dormitory". If, however, they did not share a room, Hermione's ruse is much more believable. There would be no expectation that she would have specifically discussed it with them ever, and she would simply be saying that she thought it was such public knowledge that everyone would have heard about it by now.
Another scene that would be better explained by positing that Hermione did not share a room with Parvati and Lavender is their discussion in Order of the Phoenix about Firenze teaching Divination:
"I'll bet you wish you hadn't given up Divination now, don't you, Hermione?” asked Parvati, smirking.
It was breakfast time a few days after the sacking of Professor Trelawney, and Parvati was curling her eyelashes around her wand and examining the effect in the back of her spoon. They were to have their first lesson with Firenze that morning.
"Not really,” said Hermione indifferently, who was reading the Daily Prophet. "I've never really liked horses."
She turned a page of the newspaper, scanning its columns.
"He's not a horse, he's a centaur!” said Lavender, sounding shocked.
"A gorgeous centaur..." sighed Parvati.
"Either way, he’s still got four legs," said Hermione coolly. "Anyway, I thought you two were all upset that Trelawney had gone?"
"We are!" Lavender assured her. "We went up to her office to see her, we took her some daffodils — not the honking ones that Sprout's got, nice ones..."
If they shared a room the likely would have already had this conversation at some point over the "few days"; if, however, they slept separately, this could easily be the first time they are having a real conversation since Trelawney was sacked.
On the other hand, there is also a passage that might point towards Lavender and Hermione being roommates. In Order of the Phoenix we have the following:
"Anyway, what’s up, Harry?" Hermione continued, as they walked down a flight of stairs lined with portraits of old witches and wizards, all of whom ignored them, being engrossed in their own conversation. "You look really angry about something."
"Seamus reckons Harry’s lying about You-Know-Who," said Ron succinctly, when Harry did not respond.
Hermione, whom Harry had expected to react angrily on his behalf, sighed.
"Yes, Lavender thinks so too," she said gloomily.
"Been having a nice little chat with her about whether or not I'm a lying, attention-seeking prat, have you?" Harry said loudly.
"No," said Hermione calmly, "I told her to keep her big fat mouth shut about you, actually. And it would be quite nice if you stopped jumping down Ron’s and my throats, Harry, because if you haven’t noticed, we’re on your side."
Particularly with the juxtaposition to the conversation with Seamus in the boys dormitory the previous night, this might indicate that the conversation between Lavender and Hermione took place in the dormitory as well, thus making them roommates. However, it is also possible that Hermione had this conversation with Lavender on the way to or from their separate rooms, or it is even possible that it wasn't a conversation at all and Hermione just happened to pass by Lavender and overhear her badmouthing Harry and stopped to rebuke her.
1. To illustrate this, Harry normally refers to Hermione as simply "Hermione", but when he mentions her to Dumbledore, who does not have much to do with Hermione, Harry refers to her as "Hermione Granger":
"— you can't Apparate anywhere inside the buildings or grounds," said Harry quickly. "Hermione Granger told me."