Because I don't know too much about how Tor works. I only know that my data goes through various ways or kind of zig-zag way. There isn't any risk in signing in to various websites. Yes?
closed as unclear what you're asking by Andrew Lott♦, Jens Kubieziel♦, weasel - Peter Palfrader, bastik, pabouk Jan 26 '14 at 23:05
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It depends on what user data you're entering into that website's forms. If your email address is email@example.com, and Google knows that your real name is Bob Smith, and you login to that email account using Tor, then you lose your anonymity. In other words, that target site, gmail.com, now knows exactly who you are, and if the system administrators are recording what you're doing and who you're interacting with, that information is logged and could be reported to third parties. In other words, don't perform any subversive activities if you login to a website that can identify you.
However, if you have another account that you created using Tor, one that doesn't contain any of your actual personal data, and that you've never logged into outside of Tor, none of the information you submit can tie back to you personally or to your location. For instance, if I use a fake name to sign up for a yahoo.com account called firstname.lastname@example.org and put in only fake data, and I use Tor to login to that account, no one at Yahoo knows who I am, and anyone monitoring traffic won't know what I'm doing.
A good way to learn more about how Tor works is to check out this Tor and Https diagram from the Electronic Frontier Foundation. It helped me answer the question of what my ISP and people on my wifi network can see when I'm using Tor.
Additionally to what jmort253 said, this also depends on your use-case and your threat-model.
You use the TorBrowser only to circumvent local censorship and protect your log-in credentials by logging in over https and don't fear to get arrested for posting on Facebook?
Then you can safely use it. Local observers see you connecting to the Tor network. Facebook knows that you visit it over Tor. Anyone can see what you wrote there.
You use the TorBrowser to check your mails over https secured connections from a provider that can personally identify you, but all you care is that he doesn't know where you are right now?
Then you can safely use it. The email provider knows that it is you, but not where you are. He knows that you are using Tor.