A lot of hay is being made about the forthcoming documentary The Lost Tomb of Jesus. Apparently a tomb has been found that has some names from the family of Jesus, and some people are making some pretty strong claims about how improbable it could be that it's any other family. Oh, and Jesus' bones are supposed to be present, which (if true) means not only that Jesus not only died and wasn't resurrected (or at least that after his resurrection he died and didn't ascend) but that we now have access to his DNA! See the links from Sam's post for more on the popular-level discussion of this.
There's a lot being said by people who actually have some biblical scholarship and first-century Palestinian history credentials. Tyler Williams has a good roundup of what different people are saying. I'm particularly recommending what Darrell Bock has to say, since he was involved with the documentary, and he's not very impressed with their evidence. Ben Witherington has a more detailed response. Andreas Kostenberger's is also probably worth looking at. I love Kostenberger's first sentence. Michael Pahl has further thoughts, including on what relevance the James ossuary might have to this (basically none that helps their case and perhaps some that hurts it if the ossuary is authentic.
My first impression is that this is an old story that is finding new life because a big name (James Cameron) is associated with it, and it's a story that scholars have already looked into carefully and dismissed as not really showing very much. There are all sorts of assumptions being made for the probability claim that this is resting on, a number of which are probably unlikely assumptions (that we should expect Jesus' parents to be buried in Jerusalem to begin with, never mind in a location that very clearly is not where Jesus was buried after the crucifixion, that we should expect to find a tomb of Jesus' family with only one of the three brothers of his mentioned in the gospels but some other male we know nothing of named Matthew).
Update: Several more excellent responses have appeared. Richard Bauckham's is probably the best I've seen so far, and it covers some of the most important issues that some of the others have only really gestured at. For problems related to the DNA issue, see Chris Heard and Mark Goodacre. Mark also looks at the statistical claim. I was a little disappointed at some of the earlier discussions of this, including Ben Witherington's, which I thought had argued too much in several places, but Mark's post is much better and doesn't try to claim as much while still making the statistical claim look unwarranted because of its reliance on a number of possible but perhaps unlikely assumptions, which would then lower the probability considerably. The paragraph beginning "perhaps this is labouring the point" is actually one of the most helpful for seeing one of his main points in brief.