Invasive trees in Australia. Some places consider osage invasive, I haven't seen an area where they are a problem, I wish they were more invasive. A friend of a fiend works in land conservation, says they sometimes spread on river banks due to the fruit floating down river.
I have seen black locust spread, due to suckering, but I don't think its declared as a weed. Its used quite a bit for shade on farmland for sheep and cattle.
There is some talk about Mesquite being a problem in Queensland. I think it was introduced for stock to graze on. Another pretty timber that can be put to good use as craft wood.
Willow is considered a weed by many. Not so much that it is invasive, but that it is non native and certain people think this is terrible, and that they must be removed and replaced with natives. Willow looks beautiful in the landscape, and does a good job of protecting riverbanks from erosion.
Chinese elm is considered a pest tree in some areas too.