I have a terrible problem with so many things reseeding, so I'm probably not the most reliable source of information but... Verbena bonariensis is the most invasive thing I have ever planted. I've been trying to eradicate it for at least 4 years, but I still got a lot of volunteers last summer. All of the little seedlings with the reddish purple center are VB, and they're all over every flower bed.
They're also not supposed to be perennial here but they winter over in my yard with no problem.
But- it's a pretty plant and attracts loads of butterflies.
Karen