Every time I see someone's photo of the ISS crossing the moon or the sun, I consider it a rare event, but with this website, it makes it seem like it happens all the time. When I checked the website for passes within 25 kilometers (about 15 miles), there was one solar and one lunar transit in the next 30 days, but there were four close passes. As it turns out, those close passes turn into transits if you're willing to travel 20 miles. So it appears that this DOES happen all the time. Go out and watch this some time, and if you get a picture of it, post it on our Facebook page. I'll be doing the same.
How to see the space station fly in front of the moon