A few years ago, I bought one of these at a nursery: http://davesgarden.com/guides/pf/go/80953/ It's a California native, and I figured I had just the right spot for it in my Seattle back yard, in a bed on the east side of my house that gets morning sun and shade for the rest of the day. Well, it's very cool looking with crazy flowers that look like space-age Alliums... but it has now taken over the whole length of the yard. Turns out, it just spreads runners in semi-moist soil, and since its leaves (and those of the other plants around it -- including Ligularia, Rodgersia, Gunnera, Hosta, Spirea, ferns,etc.) keep the ground well-shaded even in the morning, it just keeps a-growin'. I think I've managed to get rid of it in one area, but only through an experimental use of Round-Up (which I don't like to use, but it's the only way to get all the 1/2-inch-thick runners, which form a dense network just an inch or two underground). I've taken to cutting off the leaves and using an eyedropper to squirt a little Round-Up down the hollow stems. So far, so good. We'll see how much comes back next spring. Root fragments tend to form whole new plants!
I agree with you, jeeem. A friend in northern VA, who has many large and beautifully maintained garden beds, planted one or two Petasites three years ago or so. It was very slow to establish, but the third year the stuff emerged everywhere and had taken over huge sections of her garden. The large leaves, which are quite pretty, have enough height and size to shade to death anything under them. And boy does it spread! She's decided that the only safe way to enjoy this plant is to pot it, block the drainage hole, and plant the pot in the soil. That might work, I suppose; personally, I'll just avoid it like the plague.