Whether or not human flesh is kosher is actually quite a complicated issue.

IANAR, and these opinions do not represent authoritative Halacha, though they are based on what seem to be genuine halachic rulings cited online.

The laws of Kashrut with regards to animals are taken from Leviticus 11:

Leviticus 11:2-4

...These are the creatures that you may eat from among all the animals upon the earth . Everything among the animals that has a split hoof, which is completely separated into double hooves, and that brings up its cud - that one you may eat. But, this is what you shall not eat....

Well, humans don't have split hooves, and don't chew the cud. Open and shut case, no?

Well, no. you see, the verses above were very specific about their scope; animals, creatures. These verses don't mean you can't eat a carrot because it doesn't have split hooves, and there's no obvious reason why they should refer to humans either.

You might be tempted to claim that humans are animals. Well, that's true in biological terms. But these are legal terms here. Legally in the UK you can own animals, but not people. Cattle have to be transported in better conditions than people. so there's really no reason to assume that laws about what animals you can and can't eat has any impact on eating humans. Some Halachic authorities though (such as the Ritva), made the humans-are-animals move to ban human flesh. The Ritva also argued that as humans wouldn't have been ritually slaughtered, they wouldn't be kosher

Now it starts getting a little complicated.

The Gemara states that human milk and blood are kosher and parev biblically, but are banned by a Rabbinic prohibition unless it's still in the body, so people can bite their tongues without worry. Also, a tiny speck of blood, say from a cut, falling in food wouldn't make it non-kosher (unless you put it in on purpose). Some pretty heavyweight authorities, including the Ramban, the Rashba, and the Rosh, believe that if human blood isn't banned biblically, neither is human flesh. The Rosh points out that the Rabbinic prohibition against blood should apply to flesh too though.

The Rambam is of the opinion that the absence of explicit permission in the Torah passage above should be construed as a ban on human flesh, as a violation of the positive commandment to eat kosher animals. This is a less severe prohibition than a negative commandment, and is unenforceable by a Beit Din (Jewish court) but stricter than a Rabbinic ban.

A couple of other points to consider:

This means that even if human flesh is kosher, there are still no normal circumstances where a Jew would be allowed to eat it.

Abnormal Circumstances

There is one exception to most rules in Judaism; when a life is in danger. If, say, a Jew was stuck on a desert island, with no other way to survive than eat a corpse, it's allowed. The film Alive! deals with some of the broader moral issues around this solution. It's totally forbidden to kill someone in order to eat them and survive, even if they are dying anyway. It seems that it's better to eat explicitly treyf (non-kosher) food than to resort to human flesh in a life-or-death case. Respect should also be paid to the body, as much as possible, and a blessing should probably be made too.

In the case of an illness that isn't life-threatening, it may be permissible to eat human flesh as part of a medical cure. There are records of one Rabbinic ruling that allows the consumption of ground Egyptian mummy, which was used in many medicines and was believed to have healing powers. However this may be a special case, as mummies are so old, chemically treated and dry that they can no longer be considered flesh. And mummy-eating nowadays would be forbidden, as it doesn't actually help with much other than feeling really gross.

One thing that should be made clear from all the wriggling above is that the Rabbis weren't going to just let people eat each other. They were looking for different reasons to forbid it, and even without a specific biblical prohibition, they'd still ban it on the grounds that it's manky. So human flesh may or may not be kosher. But except in extreme circumstances, Jews aren't allowed to eat it.

Biblical translation from the Artscroll Stone Edition Tanach ISBN 0-89906-269-5