There have been claims made now and then of an apparent superluminal signal occuring in quantum tunneling process. Of course, quacks like to jump all over something like this and going off into their own laa-laa land to come up with their outlandish theories.
However, the issue isn't as simple, and in fact, could be explained via re-examining on what actually is being timed during tunneling. Several publications have dealt with such a thing. See the list below:
H. Winful, PRL v.90, p.023901 (2003)
M. Buttiker and S. Washburn, Nature v.422, p.271 (2003)
The most recent comprehensive treatment of this issue was published by H. Winful, where he again expanded upon his PRL paper and explained away the apparent superluminal paradox in various tunneling phenomena.
H. Winful, Phys. Rep. v.436, p.1 (2006).
Of course, this may not sit well with some people, and I'm sure there will be a lot more being discussed about this. However, the point here is that claims of superluminal tunneling is far from convincing.