I can't find the rules for the correct spelling of "e-mail." Some do ";e-mail," others do simply "email." Which is right?

You're right; different publications handle this word differently. Those who keep the hyphen and use e-mail are adhering to a precedent. E-mail is short for electronic mail. Words that are abbreviated with a single letter don't end up mashed together and usually keep their hyphens. Think of the other words that fall in this category: x-ray, t-shirt, c-section. On the other hand, those who have dropped the hyphen and use email are responding to the reality of this word's usage. Language is not static; it evolves and more people are omitting the hyphen. A look at some of the authoritative resources on style reflects this division. The Chicago Manual of Style advises the use of the hyphen. The AP Stylebook has adopted the unhyphenated version.

So, what are you to do? If you're writing for a particular publication, make the choice that publication consistently makes. Otherwise, make the choice that seems right to you. And be consistent. Don't use e-mail at one point and email at another. Make a choice and stick with it.