Himalayan Blackberry. They make so much fruit! The native Trailing Blackberry has smaller and tastier berries, but the invasive ones are just so productive.
I quite like the eastern grey squirrel (commonly black in some areas), Sciurus carolinensis. I find them quite cute and charming, in a rascally way. They’re introduced in my area.
I also love terrestrial isopods, and most of the ones encountered in urban areas in Canada are introduced; my favourite is probably good old Porcellio scaber. Admittedly, I’ve only rarely heard arguments that they’re invasive in the detrimental sense.
In terms of plants, I find the foliage of the Impatiens genus quite attractive; we have I. parviflora and I. glandulifera in my area.
Gray-headed Swamphens (Porphyrio poliocephalus) in Florida. I love all things Rallidae, and they are undeniably impressive. Their potential impact is largely unknown, but at the very least, they probably compete with and crowd out our native Purple Gallinules (Porphyrio martinica) in some areas.
I’m also a fan of Indian Peafowl (Pavo cristatus) despite their annoying vocalizations.
Black Locust (Robinia pseudoacacia) is introduced in my area, and can become invasive in untended fields. However, I love the picturesque gnarled form of some of the old trees of that species, with their deeply furrowed bark and their very fragrant chains of white flowers in the springtime. The flowers are attractive visually, as the species is in the Fabaceae. I like that the tree forms root nodules on which nitrogen gets fixed. Even the thorns are rather cool, so long as we do not touch them too abruptly.
House sparrows. They are annoying pests when they outcompete native birds like chickadees, and I don’t want to make it seem like they aren’t harmful, and imo native birds should always be considered first, but they are so resourceful in urban areas where not as many bird species may thrive. Bathing in puddles beside the road, eating goodness knows what off of the sidewalk, and building their nests in creative places. Plus, any cute chubby little bird is at least a little bit lovable, right?
@Quercitron, your description of Black Locust was so passionate and poetic:
That I had to read the Wikipedia article that you linked to, where I found:
Black locust is a major honey plant in the eastern US, and it has also been planted in European countries. It is the source of the renowned acacia honey.
So we have at least two organisms in this post interacting!
I find the domestic variant of Muscovy Duck incredibly cute. I like how much variety their feather patterns have, similar to feral pigeons. I’ve had many that are used to being fed by humans come up to me, wagging their tails in greeting (I don’t condone feeding them, but their behavior is adorable).
I know most people dislike them a lot, but the Feral Pigeon if definitely one of my favs! They have so many colour morphs and fancy plumages! I don’t get why some people call them skyrats, it makes me sad to hear someone call them that.
Donkeys. I love donkeys. I worked on a farm for 12 years with horses, but I’ve always had a special soft spot for the donkeys. I’d adopt every single feral burro, if only I could! I remember seeing an inat post of someone sitting near a donkey that was placidly standing there hipshot, relaxed, writing that the donkey was a destructive ass and should be culled. Well, that donkey could’ve kicked the poster in the teeth but chose not to, so I’d say it was a good donkey and deserves a nice family who appropriately appreciates it instead of being shot! No shade on the poster… I suppose we all have fits of anger from time to time.
I am personally fascinated by all the invasive plants that appear in my country and in Europe in general. Currently in Poland and in Europe, for example, Rosa rugosa is a growing problem.
to @Nezuko Which Flower Is Your Favorite and
”, you know that you’re supposed to HATE invasive species and destroy them at every opportunity! 
You have to admit that there are some invasive species that “rub you the RIGHT way!” 
Can you say more about that?