In the style of Jeff Foxworthy, here are a few behaviours that suggest you might be a writer. If you notice yourself doing any of these things, and you don't write, perhaps you should consider writing a few stories (before your friends and relatives call those nice young men in the nice white coats):
1. If you've ever listened to a co-worker tell you a tragic and/or horrifying personal story, and thought to yourself (or worse, actually said aloud), "That would make a great inciting incident for my vampire circus book!" ... you might be a writer.
2. If you've ever called a morgue or funeral home because you needed to know how much time dead bodies spent there between death and burial, if they smell like rot or chemicals, or whether it's possible for anyone to break in and give someone's dear Uncle Albert a fresh coat of lipstick and eyeshadow ... you might be a writer.
3. If you've ever lost sleep worrying about whether someone who does not actually exist (specifically, a character you've made up) will be able to survive the upcoming alien attack, repair a broken relationship, or save their one-and-only love from interrogation by terrorist ... you might be a writer.
4. If you've ever drawn strange looks and/or comments in public without knowing why, only to realize you have been talking aloud to yourself for fifteen minutes while you work out the latest plot snag in your WIP ... you might be a writer.
5. If you've ever written an angry letter to a publisher or newspaper concerning the three typographical and grammatical errors you found (and secretly thinking that if YOU had been the one writing the book or the article, there would not have been any mistakes, and what's wrong with publishers these days anyway?) ... you might be a writer.
6. If you have spent hours researching esoteric or specialized information on a certain career, historical event, or industrial process, just so you could get one single paragraph correct ... you might be a writer.
7. If you own more than one notebook full of fragmented stories and scribbled sentence fragments that don't make sense a week after you've jotted them down (or several random documents on your computer consisting of the same) ... you might be a writer.
8. If this sentence makes sense to you: "So I had a request for a partial, and the day after I sent it out two more queries paid off, and now I've got three agents reading material - but I'm still worried about the resolution, so I've been revising my secondary plot thread all week, and I'm thinking about killing off Jeffrey in the climax instead of sending him off to prison." ... you might be a writer.
This is by no means a definitive list of the signs of a writer. Feel free to add your own observations!