This question seems to be being asked a lot since yesterday's non-rapture events unfolded. While I'm no lawyer, my first instinct is to say, no. Not that I wouldn't like Camping to be held responsible in some way for what he's done, it's just that I don't see the legal case being made.
John W. Loftus wrote: "Someone ought to press criminal charges against him for fraud." (Where Oh Where is Harold Camping?)
Here's the thing - to prove fraud, you'd have to show that was Camping's intent and that he wasn't sincere in his belief (I think he really had convinced himself that he had cracked the Bible's end times code, however delusional that belief was) and unless there is some such documentation or paper/email trail where it can be shown that his true purpose was to rip people off intentionally, and he just devised the May 21 thing as a scam from the beginning, you can't show any criminal conduct on his part. I think the same would hold for a civil suit as well. Again, I'm not an attorney and I'm not trying to state the law here, but I just don't see any such attempt against Harold Camping or Family Radio being successful.
And anyway, Camping could always say something like, Well, God changed his mind and had mercy and all the prayers around the world have been heard and he has postponed the Day of Judgment so that many more can be saved.
In the following video, I have to agree with the attorney who said: "There's no offer and acceptance, there's no privity of contract. It's absolutely not actionable." Naturally, the "civil attorney" disagrees, but his type make their living filing lawsuits, so that's expected.