I've always been able to smell something distinctive BEFORE it rains. Don't know what causes that, but I've always thought it was actually change in air pressure that my nose is misinterpreting as a smell.
If memory serves me, that's due to the voltage between the storm and the ground turning O2 molecules into O3 (ozone), which gets spread around by the storm's winds.
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?
I have very poor eyesight, so my hearing and sense of smell are extremely acute.