Do any DSLRs support in-camera encryption of image files?

Canon used to sell a data verification kit which signed images for verification, and that had an encryption feature which worked with the EOS-1Ds Mark III and EOS-1D Mark III (only). However, the verification aspect was designed in a very poor way and has been compromised. Canon's response has been to discontinue the product and issue a weasel-word advisory admitting that it doesn't work without quite saying so.

That doesn't necessarily mean that the encryption aspect is broken, because when done right, this is actually an easier problem than verification (which attempts to sign something while hiding the ability to sign things — intrinsically flawed). I disagree with another answer here which says it's impossible to do in a practical way, but I'm not finding good documentation on how Canon's system was implemented (in general, good security has an open design) and given Canon's record here I definitely wouldn't trust it.

Lexar sold a CF card which, in combination with the Nikon D200 would require hash-based authentication before allowing access to the card. This was sometimes represented as encryption, but was not. For details, read this blog post by security expert Bruce Schneier, and the comments, but in short, no real encryption — and not available for current cameras anyway.

Even if you could properly encrypt in-camera, I'm pretty sure that in any situation where you might be incriminated by photos on an encrypted device where you refuse to turn over the keys, they'll find some way to imprison or otherwise punish you for not doing it. This is, for example, the law in the UK. And in the US, if the prosecution "knows" about the presence of incriminating files, courts have ruled that it's not a 5th amendment violation to make you turn them over. In more totalitarian situations, you might not even get that much of a benefit. (Let's say, for, example, you are located in China — there, it's illegal in itself to have encryption software on your computing devices without declaring it.)

You can use something like a layered encryption system with chaff and a false "safe" partition, but if the government thinks you're up to something, that probably won't really help.

It might be possible to add encryption to the CHDK or even Magic Lantern firmware hacks, but I think it's complicated and large enough that I wouldn't count on it. Another approach might be with an Android app, but you'd want to be very careful that the data never hits flash in an unencrypted form, and I'm not sure how the internals of the camera API works. Unfortunately, I'm not aware of any such app.

For this to be secure, you need to use a public key algorithm, encrypting with the public key and with the private key elsewhere — you'd have no way to review the images on the device at all. This is somewhat inconvenient, but no more than the inconvenience of waiting til you get to a lab to see what's on a roll of film.

If you are sure of the security of your desktop or laptop computer, you could keep the private key there — if you're planning to edit or manipulate the photos on that device, it's already the weak link, so no point in pretending it's not. In some situations, that may not be adequate, and you could leave the private key somewhere completely safe. If the key is held at home in another country, this may have other advantages, since you could plausibly say that nothing you can do can reveal the secret. (It might not go well for you, but the data would remain safe.) Practically speaking, a moderately-sized key will provide protection for all reasonable attacks, and a larger key will last until everyone alive today is dead, NP is shown to equal P, or quantum computers become a reality (which is certainly at least a while away)

However, again, I'm not aware of any camera or app which does any of that.

So, your best bet may be to keep only a very few files on cards and completely destroy the cards after use. (Just erasing, even with a secure-delete application, will not be enough, and as per your prior question, biting and swallowing the card won't do it either.) And of course, this won't protect you from other risks not directly related to the exposure of your images.