Is TOR really anonymous?

I recently came across TOR https://www.torproject.org/. Have any of you guys used it. Does it really work as it says?

Every system has it’s own shortcomings. One can only try to be as safe as possible and never completely safe. We always should choose to choose the "as safe as possible" route every time.
I remember reading about Tor last year. I think there was a news about French researchers compromising the so called "Tor anonymizer network". Don't know the details or validity of this info though. Tor makes sure full path of the traffic destination is never known. It randomizes one's part on the internet and makes it harder for any attacker to track/monitor your internet usage. I see that using Tor, the user's browsing experience can become relatively slower.

I was wondering how people who hack networks and website keep it safe from being caught. Does VPN give up the details when asked for in that kind of situation?