One of the craziest behaviors I have seen was from a murder of American crows in a big city area sidewalk I walk down frequently - occasionally, I have observed homeless and vagrants throwing stuff at them, because sometimes they sleep under the powerlines where the crows like to perch and I think the crows defecate on them or something.

It's well known they can carry grudges, but one day, as I was walking down the sidewalk, a pretty sizable rock smacked the pavement next to me, seemingly out of nowhere. If it had hit my head I would have been hurt. I finally look up and see a big crow staring directly down at me - it had dropped it from the power lines, it had seemingly been intentional, maybe as a warning, I don't know. I attributed it to malice towards the vagrants that harass them.

I was amazed at how much intelligence it would take to 1) form a grudge 2) form intent to threaten/harm, 3) formulate a plan using a weapon with cause -> effect to execute intent, 4) wait for opportunity.

I have observed a lot of very intelligent behaviors from these birds but that was the wildest one. I have seen it happen once since, so I'm convinced it isn't an accident.

Crows in country will wait for a newborn deer to be left alone in a field by their mothers shortly after birth to peck the baby's eyes out so it dies and the crow can eat it later. My neighbor had told me about this happening, and maybe a month later I saw a fawn with its eyes pecked out shortly after it had died. The doe just sat at the edge of the field by it all night. So sad, but really smart of the crows.

Crows have also been known to alert predators like wolves to easy prey so they can pick the remains.

I remember reading an article in National Geographic of how crow's brains are much more interconnected than is the norm in mammals, i.e. IIRC they have a higher density of synapses between neurons. From that article, it seems that the usual brain weight vs. body weight to determine intelligence, which seems can be used to approximate intelligence in different species of mammals, cannot be used for birds (or at least crows, which the article was focusing on).

In other words, they seem to achieve better results with smaller brains than we thought. And yes, crows (in EU) do exhibit some pretty intelligent behavior.

They're even apparently able to pass their grudges along to other crows who did not have first-hand experience with the subject of the grudge.

They plan pretty deeply - if you think about things like plastic lid snowboarding, or cup sorting games (fit the smaller cups inside the larger) and those types of puzzles, there's usually an abstract reward, whether it's fun, play, revenge, or some future food or whatnot. They tease other animals, will play fetch, demonstrate a rich emotional inner life, and all of those things can be motivations for their complex plans. Throw in familial loyalty, social dynamics, interactions with humans, and it's a recipe for glorious chaos. There's a lot more going on that doesn't cleanly map to most people's conception of birds.

Ravens are wonderful creatures.

I've seen crows pick up walnuts and drop them in front of moving cars so the tires will open them. I had heard that they will do that, but it was still something to see it happen.

Maybe you should be asking yourself what you did to piss of this corvid? They have been shown to recognize faces.

By "sizable rock" do you mean large pebble or small boulder?

Oh, crows are WAY smarter than that. If one tried to drop a stone on you, it was because it didn't like your online comments.

My understanding is crows can recognize individuals, so I would think back to what you did to piss off that crow, or that crow's friends.