If the information appears on a public web site--let's say the information (which might involve when you bought your home, how much you paid, what its tax assessment is) is on your local tax assessor's website--then by definition the information is not private. It's public. And that applies whether or not your home is for sale.
Further, anything that your agent may have listed on your local MLS can be picked up on Trulia or elsewhere (with proper permissions from the MLS, of course).
Now, if it's private information, such as your social security number or driver's license number, that's not permitted.
And if there's an inaccuracy--sometimes a property that isn't for sale gets listed as being for sale--then you certainly have the right to ask that the information be corrected.