I use a very small dose of melatonin, and, admittedly, I did use them more regularly than I probably should have (every night for a couple weeks or so), so I found them to be very mildly addictive at that point. It really wasn't too hard to break that addiction, though. I think the only reason I kept taking it for so long was because I needed a way of getting to bed early enough to get enough sleep before my early morning classes, and my body wasn't doing a good enough job of adjusting on its own. >_>
That being said! I've never had any other side effects from the melatonin. Like others have said, it's the same chemical that your brain naturally produces to fall asleep, so there's not much harm that can come from it. I just see it as a tiny little nudge to help get you in that direction if your brain's not producing enough of it to get you to sleep.
Oh, and I only started using them because my sleep schedule was way out-of-whack and I could never get to sleep at the right time -- and taking them for a week or two definitely helped that. Got me back on a regular cycle. ^^ I mean, I was still a bit too much of a night owl for the melatonin to help me get to bed early enough to get a good 8 hours before I had to get up at 6, but, you know. And if you're really worried about addiction, then try taking them only some nights of the week instead of all of them like I did. Oh, and start with a low dose. I never went any higher than 3mg and it worked pretty well for me. Although, you might need to go slightly higher depending on how bad your insomnia is. Just be sure to not go any higher than you really need.