There is some variation in how sensitive people are to individual odors. Picking up the ozone smell before storms seems to be sufficiently rare that a lot of people end up wondering if they're the only one.

Anyway, as I said, the ozone is produced by the electrical activity in the storm--if you're curious, you can get a smell of ozone off of artificial sources of high-voltage electricity as well. Hanging around a Tesla Coil or Van de Graff Generator ought to do the trick.

And hey, look at it this way, it's not the storm itself you're noticing--you're actually smelling lightning. How cool is that?