Hermione's parents accompany her to Diagon Alley when she goes to meet Ron and Harry to buy supplies for the coming school year. They seem like nice people – maybe a bit nervous around magic, but willing to give anything a try. Mr. Weasley is immediately excited to meet them, since he loves Muggles. Still, when Lucius Malfoy finds Mr. Weasley speaking to the Grangers at Flourish and Blotts, he uses this as further proof that Mr. Weasley is not behaving like a "proper" pureblood wizard should.
In an interview, J.K. Rowling gave a little more background on her thoughts about Hermione's family:
When I first made up Hermione I gave her a younger sister, but she was very hard to work in. The younger sister was not supposed to go to Hogwarts. She was supposed to remain a Muggle. It was a sideline that didn't work very well and it did not have a big place in the story. I have deliberately kept Hermione's family in the background. You see so much of Ron's family so I thought that I would keep Hermione's family, by contrast, quite ordinary. They are dentists, as you know. They are a bit bemused by their odd daughter but quite proud of her all the same. (source)