I guess I get to post the first essay of the new year, then. :^)
Whether Peter Pettigrew is a pure-blood, a half-blood, or a Muggle-born has never been explicitly stated either in the books or in any of JKR's interviews. However, I think it is possible to take what information we do have about Peter and make a strong case for one of the three possibilities over the other two.
I. A Muggle-born Death Eater?
The following quote has caused more than a little speculation in the HP fandom:
Snape's ancestry is hinted at. He was a Death Eater, so clearly he is no Muggle born, because Muggle borns are not allowed to be Death Eaters, except in rare circumstances.
(J. K. Rowling, Edinburgh Book Festival, August 2004)
Since HBP has been released, some people who either misremembered or had only heard of this quote second-hand believe that Snape is the Death Eater with Muggle heritage that joined the Death Eaters due to rare circumstances. However, the quote clearly specifies that Snape is not one of those exceptions. Also, Snape is a half-blood (since he has a witch for a mother and a Muggle father) not a Muggle-born. There are likely to be a number of half-bloods among the Death Eaters. Pure-bloods only make up 25% of the Wizarding population and not all of those agree with Voldemort's cause, making it likely that they will in some cases overlook an insufficient pedigree as long as the candidate is willing to espouse the cause with sufficient fervor.
What I find interesting about the quote is that JKR allows for the possibility of Muggle-born Death Eaters at all. After all, a Muggle-born joining the Death Eaters makes about as much sense as an English protestant joining the IRA. So there is likely to be a reason she didn't simply deny the possibility. I've come up with two scenarios on how it might come into play. The first is that Harry will be betrayed by a Muggle-born classmate who's secretly working with the Death Eaters. I don't find this scenario to be that likely because there just doesn't seem to be much of a set up for it in what's been published so far and we've only got one book left. The other, more likely, scenario is that there's an existing Death Eater who is a Muggle-born who joined the Death Eaters due to unusual circumstances.
With only one book left, we should know who the prominent Death Eaters in the story are by now. It would have to be one of the major players, because who cares if J. Random Death Eater is or isn't Muggle-born? And there is one Death Eater who stands out from the rest. Someone who was recruited for a very specific, very important task. Someone no one's ever accused of actually believing in pure-blood supremacy. I am, of course, speaking of Peter Pettigrew.
Theorizing that he's Muggle-born from an interview quote is all well and good, but the real question, as always, is if what we see in canon fits with the theory. And while there's no smoking gun, so to speak, there are several things that I've noticed in canon relating to Peter that are consistent with or could be explained by Peter being Muggle-born, and very little that might conflict with the notion.
II. Evidence for Peter being Muggle-born
A. Why Peter Wasn't Suspected As The Spy
"But you, Peter -- I'll never understand why I didn't see you were the spy from the start. You always liked big friends who'd look after you, didn't you? It used to be us... me and Remus... and James...." - Sirius Black
(PoA, US pb, pg. 369)
So why didn't he see it? If Peter was seen as being so weak and needing looking after by the others, why does it seem like none of them even considered the possibility that Peter might have been pressured into passing information to the Death Eaters? Instead, not just Sirius but James and Lily felt confident enough in Peter's loyalty that they agreed to make him the Potters' Secret Keeper. Some people think James and Sirius didn't consider the possibility because they took Peter's loyalty for granted, but then how do you explain why Lily went along with it? Also, by all accounts it was a very paranoid time, and being targeted by Voldemort would have made the Potters even more paranoid than most, particularly after they learned that one of their close friends was a spy.
If Peter's Muggle-born, however, all they would have had to do is overestimate Voldemort's prejudice and dismiss the possibility of him using a Muggle-born as a long-term agent. That would rule out Peter as a possibility, James was obviously not the spy, which leaves Sirius and Remus suspecting each other due to process of elimination. Once the seeds of suspicion had been planted, any suspicious behavior on Sirius' or Remus' part would have been taken as evidence of the other's possible betrayal. All Peter would have to do to continue to escape suspicion is to make sure he didn't draw attention to himself in a way that would make the others reconsider their initial automatic ruling out of him as a possible spy.
And if the suspicion between Remus and Sirius started out from not having any other candidate for who the spy could be, their easy forgiveness of each other after the truth comes out in PoA makes a lot of sense. After all, it's hard to blame some one for coming to the wrong conclusion using the same line reasoning you used to come to an equally incorrect conclusion.
B. The Framing of Sirius Black
Peter's framing of Sirius Black for his murder and the betrayal of the Potters' was obviously a deliberate act. He had a head start on Sirius, there was no reason for him to be wandering around on a Muggle street (in human form no less) instead of already having secreted himself in some safe little hidey hole unless he wanted Sirius to find him. And for Peter to have come up with the plan and thought it had enough chance of success to be worth implementing, he would have needed to know two things. The first thing is where Sirius would be likely to look for him. The second thing he would need to know is enough about how Muggle streets are constructed to figure how to blast a hole in one that would let him escape through the sewers. (I mean, do you think Peter would put himself in wand's reach of an angry Sirius Black without a quick escape plan already in mind, just waiting to be implemented? I certainly don't think so.)
Now, if Peter's Muggle-born then it follows that Sirius might expect Peter to try to hide in a Muggle area since Peter would be more familiar with Muggles than the pure-blooded Sirius and have an easier time blending in. It would also explain how Peter would know enough about Muggle streets to pull off the creation of his escape route. (And pull it off in such a way that he convincingly appeared to die, as well.) We've all seen in the series how poorly educated those who are raised in the Wizarding world are about Muggle things, after all.
C. No Faith in the Cause
No one ever suggests that Peter truly believes in the Death Eaters' agenda. We never see Peter do or say anything to indicate he hates or looks down on Muggles and Muggle-borns. All of Peter's claims of loyalty or faithfulness in GoF are based on giving assistance to Voldemort himself, not to the Death Eaters' cause. Voldemort, who we know is an accomplished Legilimens, states that the only reason Peter returned to him and assisted with his resurrection at all is because he was afraid of Sirius and Remus managing to hunt him down. Sirius doesn't bring it up as a possible reason for Peter's betrayal of the Potters, not even in a mocking fashion before proceeding to his true accusations of what Peter's motives were. Of course, Peter could be in Voldemort's service purely out of fear without being Muggle-born, but it's certain interesting that he doesn't try to toady up to Voldemort by falsely claiming faith in his cause, and that no one sees genuine belief in the Death Eaters' cause to be worth suggesting as a motivation for Peter.
D. Peter's Treatment by the Death Eaters
"We... we are alone, aren't we?" Narcissa asked quietly.
"Yes, of course. Well, Wormtail's here, but we're not counting vermin, are we?"
(HBP, US hc, pg. 23)
Peter is obviously kept on a short leash after Voldemort's resurrection, because we don't see him in either of the battles with Death Eaters shown afterwards, even once the Ministry acknowledges Voldemort's return and Sirius dies, negating any need for Peter to remain in hiding. The one time we do see him, he is stuck acting as a servant to Severus Snape, who calls him vermin and treats him with utter contempt. Bellatrix and Narcissa, who are present at the time, don't even deign to acknowledge Peter's presence. He isn't treated as an equal by the other Death Eaters, or even a normal subordinate. No, he gets treated as you might expect a house-elf to be treated. And despite his protest to Snape that he could speak to Voldemort if he wanted to, Peter obviously doesn't have enough pull to get himself out of this situation into a better of to make the other Death Eaters give him any respect.
And this is the case even though it was Peter who sought out Voldemort and helped him regain his body, albeit for his own selfish reasons. Peter being seen as a weak wizard and being a known traitor to his previous friends just doesn't seem to be enough of an explanation for this situation to me. But it is the kind of treatment I would expect to see of a Muggle-born who'd made himself useful enough to end up being allowed to serve Voldemort and his Death Eaters. They wouldn't see a 'Mudblood' as being any more their equal and worthy of respect than a house-elf, after all, even if he has agreed to serve his betters.
III. Elements That Might Contradict Peter being Muggle-born
A. The Order of Merlin
"...Pettigrew received the Order of Merlin, First Class, which I think was some comfort to his poor mother." - Cornelius Fudge
(PoA, US pb, pg. 208)
This is the one and only piece of information we've gotten on Peter's family in the books. Some people think that this passage indicates that Peter's mother, at least, had to be a witch. But we know that the parents of Muggle-born students are allowed to know of the Wizarding world, so why wouldn't they have given his mother the Order of Merlin medal and let her know how her son died if she was a Muggle? And we only have Fudge's opinion on whether it was of any comfort to Peter's mother, with no indication that he was actually there when she got it to see her reaction. So while this statement doesn't support Peter being Muggle-born, it's not truly inconsistent with it, either.
B. Why Hasn't Anyone Said So?
So, one might ask, if Peter's a Muggle-born, why hasn't anyone said so in the books? Well, characters' ancestry is rarely brought up unless if there's some type of point in doing so. After all, we've never been explicitly told the ancestry of the Patils or Lavender Brown, AFAIK, or Cho Chang or many other characters. We only know that Remus Lupin is a half-blood because JKR stated it in an interview, and we didn't find out Snape was a half-blood until HBP. So Peter is hardly unusual in not having his ancestry specified. And I can't really think of any reason for JKR to want Harry (and we readers) to know that Peter's Muggle-born so far. It's definitely possible that we'll end the series with Peter's ancestry still being unstated, but having been an influence on his actions none the less.
Any single point of evidence I gave above has other possible explanations, of course. But Peter being Muggle-born pulls many of the questions and oddities surrounding his betrayal of the Potters and his current place with the Death Eaters into a coherent picture, instead of requiring them each to be explained individually. It also provides a good explanation for JKR's reference to Muggle-borns being Death Eaters under rare circumstance.