Well, that depends. To me, a hobby is something you can put aside both physically and mentally when you need to, like when you’re at work. An obsession is something that you can’t put aside no matter how much that would help you in your work/social life/etc. For instance, I am obsessed with my writing. I spend the vast majority of my work or “leisure” time thinking about new story ideas, places the plot of my current book is going, whether I should change one single word in chapter seven (I have memorized the entire book, since I am obsessed with it). I write little fanfictions in my head based on the characters in my book and decide how to incorporate them. I do this all while working, and I can’t put it out of my mind if I want to (although, really, I don’t want to). Conversely, my hobby is knitting. This means that I don’t have to think about knitting if I don’t want to; my thoughts only drift back to it when I guide them that way, or if I am really bored and just thinking about a whole lot of different stuff. I like doing it a lot, but if I were forced to give it up, it wouldn’t kill me, like it would if I had to give up writing. That, to me, is the difference between an obsession and a hobby. I agree that most of what people are listing here as “obsessions” really aren’t, though.
Getting back to the OP, my mom fits–she has no hobbies at all, she just pretty much sits in front of the TV all day and waits to die. Sounds blunt, but it’s true. My dad is only a little better; he plays golf, and I guess you could say he’s obsessed with medicine insofar as he’s a diagnosed hypochondriac. But then, that’s a bad obsession, unlike writing. My sister really doesn’t have any hobbies/obsessions outside from the flute (which she’s only interested in because my parents made her take up an instrument, I doubt she’d have developed this hobby on her own) and Internet chatting (again, an unhealthy obsession). Actually, I think there are probably more people without intense driving interests than those with–it’s just that the people with IDIs tend to hang around each other to such an extent that we forget there are people in the world without any passion at all, since we’re obviously not going to be compatible with them. Different worlds, and all that.