There's sometimes a stigma associated with listening to recordings of pieces one is playing. The fear seems to be that a student will simply imitate the artist on the recording.
There is a well founded basis for this fear. If you compare the varieties of interpretation now to early recordings from the past, you'll find that things have become more and more homogenized.
But beyond this fear lies the fact that by not listening to a piece you can seriously slow down your rate of progress. The reason is simple: the better the aural picture you hold of a work, the more information your ear has at its disposal to integrate all the elements of playing. In the end, it's our knowledge of what a piece *sounds* like that holds everything together.
A secondary benefit of recordings is that, far from limiting an interpretation, they can open you up to unconsidered possibilities; especially if you make a habit of listening to many different interpretations from different time periods. The key is to judge for yourself.
"You know, I'm not a natural pianist. I never was.", said Rudolf Serkin to his student Lee Luvisi, " It always came very hard to me. If I don't work hard I can't play. I'm no different from most musicians; I don't always feel like going out there and playing, But I want to be ready when that happens so it's still above average." *
Serkin, who by his own admission was not a naturally gifted artist, wasn't just a great pianist, but one of the most influential musicians of all time. Can we really attribute much of this success to an extraordinarily high work ethic?
Lately I've been reading a book recommended to me by a student called Talent Is Overrated. The author, Geoff Colvin, answers this question with an emphatic yes. Colvin makes a strong case for the value of consistent practice over innate talent; an idea with far reaching implications in music. He supports his argument with a host of different studies--many of them dealing with classical musicians.
I was particularly struck by an extensive study conducted with violinists of varying playing abilities. To make a long story short, the statistically significant factor differentiating each level of player was the amount of time engaged in deliberate, goal-directed practice. By "amount of time" I mean not only average time per day, but the cumulative amount of time spent practicing in each violinist's life.
Is this surprising? Yes and no. No, because we all know that "practice makes perfect". Yes, because we also know, or think we know, that musical ability is strongly dependent on some kind of innate talent. What Colvin suggests is that what we interpret as talent is more often than not simply the result of well applied practice over the course of many years.
In general, I agree with Colvin-- but I'd grant a little more ground to talent than he does. I've known extraordinarily gifted musicians who could do things far outside the provence of high-level abilities. For instance, people with nearly photographic musical memories from an early age. I've also observed some young children who seem to exhibit a better sense of things musically than their peers. But having said that, I've noticed that people give far too much weight to talent, sometimes too much to hard work, and not nearly enough to intelligent hard work.
In Talent Is Overrated, Colvin does seem to conflate correlation and causation. The fact that the most talented performers practice the most doesn't mean practice is what makes them the most talented! In many cases, people with a knack for piano end up practicing more simply because of the joy of doing something that they're good at.
Of course the opposite is just as true. I've had tremendously talented students with such poor a work ethic that their performance was far below their potential level. Similarly, I've been astounded many times when pupils that show little early promise take off after a period of sustained work.
I was this sort of late bloomer and, in fact, I'm fairly certain that my early teachers would be astounded at my current musical career. At 11 or 12 I was simply a mediocre piano student, and it wasn't until that age that I started practicing hard and, over the course of several years, reached a high level of playing. It occurs to me that if someone had told me at 11 or 12 that talent was simply a matter of inborn traits--something that other people had in greater degree than myself--I might have never have practiced so hard. The best path then is just to craft your abilities as best you can. Let someone else worry about who is and isn't talented, and you can just enjoy the music!
*Quoted in "Rudolf Serkin: A Life" by Stephen Lehmann and Marion Faber. Oxford, 2003: 210.
. The author, Geoff Colvin, answers this question with an emphatic 
