I've often thought about this, too. We have had up to 10 cats (9 now), and DH is often away at work, so I most likely will have no help. I try to war-game how I'll trap 9 crazy cats in a panic, and THEN either shelter in place or, if it's an evacuation situation, get them all into my small car. My car is 13 years old, and I'm seriously considering a mini-van or SUV for the next car--even just to make vet trips easier. And, if the shelter won't allow pets, I'm staying here with my cats.
We have tornado sightings here once or twice per year, but no real damage (yet). As we have no basement, I'll either go with the cats in the under-stairs pantry (small!) or in the stairwell (usually the most stable part of a house). We could also hunker down in the foyer; the only window is in the door, but it's safety glass and not too close to where we'd hunker down. I only have 1 window-less room, but that's the laundry room--next to the garage (garage doors are usually the weakest door in your house)--and the garage has a window!
I'm so happy to see that everyone is ok!!!