Isn't it great that you've got 5+ answers here already, and none of them appear to provide the same answer? The definition of a fixture seems to be alluding people. Carlos stated it best, however, and plain and simple, a fixture is anything that is attached to the home, and requires a tool to remove it. ANYTHING attached that requires a tool to remove it is a fixture.
That TV bracket is clearly attached to the wall with some kind of screws. Therefore, it is a fixture. The TV, is probably attached to the bracket via screws, probably requiring an allen wrench to separate it from the bracket. Therefore, the TV becomes a fixture. Even if the bracket is a 2 piece kind, with part attached to the wall, and the second part attached to the TV, since the entire bracket is a fixture, it makes the entire TV a fixture. A few TV's are not in any way attached to their bracket, but instead are hung, like a picture, on the bracket. If that's the case, the TV would be treated just like any other piece of art, and you can take it with you. But does the buyer know that? Probably not.
So, assuming your TV would be considered a fixture, what do you do? If you want to take it with you, make sure the purchase contract states that it does not convey. If the original offer doesn't state anything regarding the TV, be sure to counter-offer your intentions. The MLS listing, signs in the home, and verbal conversations all have no bearing over what is or is not a fixture. Only the contract. So put it in writing, and everyone will be happy.
If it's not in writing, I know a lot of listing agents that are buying their clients flat panel TVs. It seems to be all the rage these days...