Doesn't exist for average Joe-s but for people which are very experienced in computers, it exists and can be accessed by anyone who wish to remain anonymous on the net, using TOR browser and TAILS version of Linux which is a live OS with TOR incorporated, chances are very slim to find who you are and for that the government needs to spend lots of money. So yeah if you use Bitcoin by using the 2 systems above, it can become anonymous although it can be tracked later on but not in the beginning. Any criminal can be in some paradise Island, the moment its address become identified with its real IP so yeah in the end bitcoin can be anonymous, but as per se its pseudo-anonymous.