I have a year and a half-old independent appraisal of my house that values it at $173,800, which is what the bank used to approve my mortgage. Zillow values it at $167,902. Trulia uses the county assessed price for tax purposes, and values it at $161,790 (the county hasn't changed value of the house in 2 years). Although Trulia also gives you the average list and sales price of similar homes in the area ($225,536 and $193,875, respectively).
If you were looking to sell your home, Trulia seems to give you more information. I'm surprised that Zillow is as accurate as it is--this is new; Zillow used to have the house severely undervalued.
Since you're looking to figure your net worth, it's best to use an independent appraisal, but that costs money and ultimately wouldn't be worth it unless you were looking to buy or sell. The county's appraisal is hit/miss. Sometimes counties will play with numbers. Apparently, in certain areas this year, my county undervalued homes to give folks a break on property taxes. My home value stayed the same, though, and some home values were reduced for legitimate reasons (foreclosures in the area). When a county is trying to be accurate (which is the majority of the time), how accurate it is depends on how they go about appraising homes. In my area, it's a walk-by appraisal. There's not a lot of thought, and a lot of homes are valued at the exact same price simply because they are relatively close and have the same square footage. There's no factor for improvements and the appraisers have no idea what the house looks like on the inside, but it's the best they're able to do given the circumstances.
Ultimately, you may want to meet somewhere in the middle of average sales price in your area and whatever value the county has set for your home. If you've done a lot of improvements, you may want to skew higher; if your home needs a lot of work, you may want to skew lower.