It truly depends on the area and the accuracy of the information Zillow is obtaining. I have found some "Zestimates" to be within a few hundred dollars of appraisal amounts and some are thousands off.
As Zillow grows and becomes a more robust real estate website with more and more sales data, I believe the Zestimate value will slowly come in line more and more with actual values.
I can give a true for instance... We have a client who just did a refi on their property and the Zestimate for their house was within $5000 of the appraised value. So not too bad.
As with other answers, if you want a true value of your home in the current market, contact a REALTOR. A licensed agent has access to the most recent and up-to-date data and give you a snapshot of the market at any given time. With that said, you're home is only worth what a buyer is willing to pay. That, unfortunately, is just the way real estate goes.