I'd take insurance and other important documents, and irreplaceables, such as family pictures. Some drinking water and snacks and a first aid kit would be good in case you get trapped down there for a while. With plenty of time, I might take some UFO's or finished things that took me a lot of time to make, and maybe some small handwork to do while waiting. I figure the possibility of losing things that can be bought again is why we have insurance, but yes, of course if there's plenty of time, saving anything you want to, just so you don't have to go through a loss, makes perfect sense to me.
Our insurance company has a link on their site to an independent site that lets you archive pictures and descriptions of household belongings and valuables in case there is a loss. Taking the pictures and storing copies of them away from home - for example, online or at a trusted relative's house in another city - could be extremely helpful if you ever have to file a claim. Write down serial numbers, dates of purchase, what you paid, and other details. You could also make an inventory check-list, which your insurance company would likely provide.
I hope you have no more tornado scares!