I hesitate to include native plants in an "invasive species" section since they are not technically invasive. They're not even what I myself consider invasive.
I include these only because so many people mistakenly describe them as invasive.
We have some of these overly eager native plants. I've heard people refer to them as "invasive" because they're invading their yard beyond their allotted space. I call them "exuberant" or "enthusiastic," but they are NOT ecologically invasive plants.
NOTE: I'm referring to plants native to our region. Certainly "native" plants that are native to, for example, the Pacific Northwest are not a native plant in our region, so they could indeed accurately be described as invasive in Central New York.
Enthusiastic native plants may sometimes be annoying BUT don't create the dangers posed by non-native invasive plants.
I grow these enthusiastic plants when I judge their benefits to wildlife or my own pleasure outweigh the annoyance of keeping them in bounds.
I definitely enjoy joe-pye as much as butterflies do! Taking a little time to cut some of them back in June and pull out extra seedlings is worth the small effort to me. If I want fewer seedlings, I also cut off some of the excess seedheads, although not all since birds enjoy these seeds.
The prime example in our habitat garden at the moment is jewelweed (Impatiens capensis). As the name implies, it's the native version of the non-native impatiens that's widely sold as a bedding plant. Yes, it can be annoying because it spreads enthusiastically.
But in its favor, it's a wonderful nectar plant. The hummingbirds and bumble bees adore it, and I find the little hanging blossoms intriguing. (I and others also take some child-like pleasure in touching the ripe seed pods to watch them scatter their seeds—the reason that its other common name is touch-me-not.)
For me these benefits far outweigh the minor annoyance of having to pull out excess plants. I might feel differently if that were a difficult job, but these plants have very shallow roots, so with a minor tug I can pull out handfuls of the extras and compost them.
Perhaps another example could be some of the goldenrods (Solidago). These don't spread nearly as much as jewelweed, but they're a bit more difficult to dig out.
On balance, though, their beautiful flowers and essential role in providing nectar for fall pollinators (including the monarch) make them far too valuable to give up.
Poison ivy showing the larger leaf petiole of the middle leaf, a characteristic, we're told, of poison plants in general
Poison ivy is native and a fine habitat plant—if you're not a human. Yes, it's native, but if you have a regular-size yard, it's hard to co-exist peacefully with this plant. (If you have acres, perhaps you can leave it be in some areas.)
We don't have this plant in our yard here in Central New York fortunately, but our family has had run-ins with it in North Carolina.