I live in NorCal. In a hot real estate market, Zillow is not all that accurate. Your market may vary, but here is a personal example. In March 2013, I listed my townhouse for 539k. I received multiple offers for 600k within the first week*. It closed in April, 2013. Since then at least seven people in the HOA have leveraged that price and have closed for even higher prices.
Zillow has consistently listed my old home's value at closer to my asking price than my closing price, despite newer sales for even higher prices per square foot. Finally, after almost eighteen months, Zillow is just now valuing it at 603k. Based on recent comps, it would probably fetch somewhere around $660-$675 in today's market.
Conversely, Zillow claims the home we closed on in August, 2013 is now worth 172k more than we paid for it. In this case, probably way too high.
So, Zillow is a good source for past history, current listings, and armchair shopping. It is not a reliable indicator of your home's worth. If you are seriously looking, seek out an experienced realtor. They know the local market much better than Zillow.
*Yes, I had multiple offers. I chose the young family who included a lovely cover letter and a letter of prequalification with their offer. If you're ever in a bidding situation, write a cover letter with your offer. It works.