When I lived in Louisiana, there were a couple trees in our yard that just grew there. For the longest time I had no idea what they were, but they were pretty and shady and I would not object at all to having them planted in my dream-yard (of the dream house that I hope to some day have...). One type was mimosa and today (thanks to
http://www.arborday.org/trees/whattree/WhatTree.cfm?ItemID=w33a) I found out the other type was a catalpa. Where I'm from (and probably a lot of other places) these are both considered weed trees, so it was extremely hard to find out what they were as most nurseries wouldn't carry them, and most of the people I knew didn't care...
Yay! Now I know what to look for in the future. :D