What is a weed? What's weedy in my garden is not necessarily in yours. That depends on climate and soil and other factors.
Here are some examples of problematic weedy garden plants in my garden.
1) Campanula and Impatiens
2) Campanula lactiflora
3) Impatiens glandulifera
The taller growing campanulas like C. lactiflora are vigorously growing and prolific self seeders everywhere.
The annual Impatiens glandulifera dominates in moist soil.
4&5) Telekia speciosa pops up especially in the paths.
New England USA
One rampant spreading weed here is Veronica Georgia Blue. I have a mix of the standard taller perennial Veronicas, they stay in clumps, but seed heavily everywhere. Veronica incana died out; mised, but not a weed.