The phrase "electronic mail" used to refer to any message sent through electronic means, even faxes (though probably never telegrams). The term eventually narrowed to what is considered e-mail today. Meanwhile, the word "e-mail" has become so common that the hyphen has been dropping out of use. Many people write just "email."
So which is correct: "e-mail" or "email"? Language changes, and there is no universal agreement at this moment in time. Some authorities in such matters such as the AP Stylebook, for example, have declared the unhyphenated "email" as their standard.
There are good arguments on either side of the issue. The case for dropping the hyphen is simple. Because moving a finger to the hyphen at the top of the keyboard slows down typing, common usage has gravitated toward "email." And if so many people are spelling the word this way, this spelling has to be considered legitimate.
But others insist on keeping the hyphen. First, many hyphenated words like t-shirt, x-ray, and g-string retain their hyphens for clarity. The spellings "tshirt," "xray," and "gstring" look weird and cluttered. So for the sake of consistency with other spellings and overall readability, the hyphenated "e-mail" should be favored.
Also, the unhyphenated "email" spelling would instinctively be pronounced differently. Following the pattern of words like "emancipate" or "emerald," the letter e would sound like eh and not ee — that is to say, ehmail. A reader needs to take a moment to remember that a word written as "email" is an exception to how common English spelling patterns work.
As for me, I personally come down on the side of "e-mail." I like the hyphen.
Sure, including a hyphen for such a common word is a bit of a hassle for someone typing fast, and as I professional writer, I type a lot. But not having the hyphen slows down a reader who unconsciously expects to see it there. Someone has to make the extra effort, either the reader or the writer.
In my opinion, the responsibility falls on the writer. The purpose of writing is communication, and good writing aims to make ideas as easy as possible for the reader to understand.
This discussion about whether to include the hyphen in "e-mail" may seem a little pointless, and perhaps it is. But to me this issue is about more than the spelling of a single word. Instead, there's a general principle at play here. Anything that forces readers to work harder, even if it's a single dropped punctuation mark, makes them a that much less willing to listen to what the writer has to say. As a result, it makes them that much more willing to turn a page or click away to somewhere else.