Pffft, try avacados here in SoCal! Just kidding! They're not really a threat to cyclists unless you don't watch where you're going. Still, not many avacado trees grow on the side of streets.
We have small acrons here, so they don't bother me. We do have some sort of tree that have these spiky balls. One or two can take you out if you're not careful. They don't cause flats, but they could make you wobble or fall if you run over one.