The version of Tor currently shipped in Tails does not protect your anonymity as it should. This vulnerability is critical.
Until a future version of Tails is released (soon), the only way to have Tails protect your anonymity is to upgrade Tor every time you start Tails, by following the instructions bellow.
(Every time, really? Sure. Tails is amnesic: any change you make in it is lost upon restart.)
To upgrade Tor, start a Root Terminal from the Applications → Accessories menu, and type the following command in there:
apt-get update && apt-get install tor && service tor start
... then type Enter, and wait until the upgrade is completed, which may take a few minutes. At this time, the Vidalia icon on the top right of the screen should have changed from the usual green onion to a grey, red-crossed one. Right click on it and choose Exit in the menu that opens. Then, start a new Vidalia from the Applications → Internet menu.
Once this is done, you can safely use Tails as usual.
Want details? See the Tor project's blog post about it.