I think it's an outdated view that email can only be used as an uncountable noun and one which most native speakers do not subscribe to any more. When email was invented as a means of communication it was treated as a mass noun, and thus uncountable e.g. I received a lot of email today. However, over time people started to use 'emails' as a shorthand for 'pieces of email' or 'electronic mail messages. I think pretty much everybody does this. 'The usage dictates the convention and language can adapt over time to accommodate this. You'll hear native speakers very commonly say things like 'I have five emails in my inbox.' So it can be used as an uncountable or countable noun, depending on what you want to say.

It's a relatively new word and its usage is evolving. Don't worry too much about it, just do whatever you notice that other people are doing. For example, there's no general agreement on whether to spell it with or without a hyphen. ahdictionary.com is showing me e-mail with a hyphen as the entry, with email as the variant, but I think it's the other way around! The tendency is always for punctuation to disappear. I used a hyphen myself ten years ago, but I've stopped using it. I'm a U.S. native speaker who's been using email in various forms since the 1980s, and I can say only that I personally use it both ways, countable and uncountable. (This isn't unusual. The same thing is true of some other nouns: "Your aquarium is full of fish!" "Yes, there are eight fish in my aquarium.") All I can say is that these are four examples of ways in which I personally use the word: "I'm going on vacation and won't be checking email very often." "Yikes! I just got back from vacation and I have 956 emails in my inbox." "I'm getting too much email from merchants who didn't give me a chance to opt out." "I'm getting too many emails from merchants who didn't give me a chance to opt out." (Yes, I could say it either way and I can't tell you why I might choose one or the other). "I sent you two emails about next week's plans; did you get them?" "Kimball sends me email almost every day." "My email is down today." (Here, email means "email system.") "My email is [email protected]". (Here, the word "email" is being used to mean "email address.")

The word "e-mail" originally is a form of communication, that's why it's uncountable, originally what you send and receive is an "e-mail message", so the plural form is "e-mail messages" ,but in everyday usage, people used the word "e-mail" as a short for "e-mail message" just because it's shorter and easier to use.

This is practically a joke, but there is a very obscure English word, "email" without a hyphen, that is found in big dictionaries--I'm using Merriam-Webster's Third. It got some attention when the word "e-mail" was coming into general use and people were arguing about usage and spelling. I don't think one in a million people ever heard of this word before that--and I don't think one in ten thousand people know it now! It's a loan word from French, and Merriam-Webster says it means "a moderate bluish green to greenish blue that is lighter than gendarme, deeper than cyan blue, and duller than parrot blue--called also 'bleu Louise.'" Yes, of course it is. Sure. :) Of course, it is pronounced with an approximation to French pronunciation, AH-mee or something like that.

Actually, I have just found a dictionary saying that it can be both countable and uncountable.