No, it's not really used in everyday speech. "Everyday writing" is a little ambiguous because it's mostly the form of the writing that determines the tone. To address your edit, it would be weird to use まい in a message to your friend, but I wouldn't be surprised to see it in work correspondence if only because that tends to be more formal in general. The more formal it is the less unusual it is for a term like まい to appear. Generally it's just not a spoken term and is reserved for more formal situations, however if you were to use it in conversation you wouldn't be misunderstood or anything.
In my experience though it is a term that just isn't used much at all regardless. You should be able to recognize it, of course, but I don't think I've ever seen it used outside of writing, and even then I think I usually see it as a line from a character with a particularly formal speaking style or something of that sort. As the comments note, it has a very old fashioned sort of feeling, although it does make some modern appearances in the phrase ～じゃあるまいし.