I'm the Queen of tornado preparedness here in Oklahoma. We've got a safe room in the garage (thank you, Ol' Boy) big enough for us and our three cats in their comfortable, private carriers. In it there're enough supplies for at least three days without access to the outside world:
money (in small denominations! and include some coins)
food (freeze dried, MREs, canned, etc., rotated by date so it doesn't get old)
water (and stuff to purify water if you run out)
fuel for a propane hot plate
hot plate
tv with UPS
lanterns
lots and lots of batteries
waterproof matches
radio (both hand-cranked and battery-powered), both with weather band/alert
change of clothes
blankets
rain ponchos
plastic sheeting/tarp
tools (hammer, plyers, screwdrivers, wrenches for shutting off gas/water)
Nails, screws, rope
work gloves
candles
First Aid kit and instructions - PLUS any prescription meds
Safety glasses
Dust masks
Port-a-Potty and supplies
toiletries
TV tray and seats
Kitty food
Kitty potty
hard-wired telephone
whistle, signal flag
can opener
bottle opener
pocket knife
scissors
compass
copies of important papers (insurance, etc. - including an inventory of your home)
fire extinguisher
books and games
plastic bins to keep all this stuff packed neatly
Gosh... I know I've forgotten SOMEthing...
Oh... and if you have babies/children, you've got to have them covered, too, of course. I just don't have a clue what that would include.
ETA: A generator is very nice, too... but we keep it just outside the garage door (and hope it doesn't get blown away in the event of a really nasty tornado)