These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Awesome Music: The soundtrack is filled great scores that all fit the tone of the game. Though most of them in a somewhat melancholic way.
Demonic Spiders: Quite a few. AI War is a game that takes pleasure in torturing the player.
Astro Trains stand out following update 6.006. The update is even called "The Pain Train" by the developers. Astro Trains - AI units that will rush back and forth through vast stretches of space to move between AI Train Stations - are very fast and Nigh Invulnerable to boot, to the point where the Lost Superweapon Golem starships are considered one of the few ways to reliably destroy them. That or high-Mark Spire Implosion Artillery, which you have a limited supply of, particularly in the early game (and might not have at all, depending on what options you enabled at the start of the game). It isn't the fact that they're fast and insanely durable that makes them annoying, though. No, what makes them really annoying is what they carry. The ones that have guns are actually the least worrisome, since all they'll do is shoot your turrets a bit, and maybe inflict light damage on your ships. The ones that are the most annoying are the ones that apply a Status Buff to the AI or debuff your own units as long as they're in the system. Since the only real way to control where Astro Trains go is to destroy Train Stations, one or more of which might be deep in enemy territory, you can't really tell when one or more Trains is going to show up during a big battle and tip things towards the AI's side. There are also variants which use massive Tractor Beam complexes to kidnap huge numbers of your ships at once, which can be just as devastating. And then there are Cargo Trains...
For those of you who actually want to know rather than experiencing them for yourself, Cargo Trains don't actually attack you. They just bounce back and forth between Train Stations, slowly increasing the progress meter for an AI superweapon project. When this is completed, the AI gets Golems. And this can happen less than three hours into the game if you don't devote all of your resources to preventing it.
Also, depending on the plot difficulty, the Golems aren't the biggest problem. If the Astro Train plot is set to 8 or higher, you will face the Hunter/Killer (normally a unit that only appears in Fallen Spire campaign), and you will understand why normally it only appears in that campaign.
Human Marauders are also quite intimidating. While you're the leader of a faction of humans dedicated to reclaiming the galaxy from the AI, Marauders are Space Pirates who have decided to just blow up everything they can find, take the scrap, and sell it for profit. Their ships are durable and powerful enough that they can sometimes destroy AI worlds all by themselves, if the player retreats back to their own systems after they appear.
What's that? You're planning to use the Showdown Devices from Vengeance of the Machine? Then the machine will charge at you with a vengeance! The massive Exo-galactic attack force that will come towards you will include Galactic Control Ships. What makes this monstrosity the most fearsome enemy in the entire game is not the fact that it is more powerful than a Mothership (Although it helps. And keep in mind that a Mothership is already some extreme overkill when it comes to power), nor the fact that it explodes like a Mark II nuclear missile when (if) you manage to destroy them (Although that helps, too)... It's the fact that the AI sends not one, but two. And they go directly for your Home Command Station, no sidepaths, no stops, just flying towards you, in the straightest line possible, at the speed of death. Good luck dealing with them. You're gonna need it.
Fridge Horror: The primary resource in the game is metal. Metal is collected by building mines on metal deposits, which are found in massive fields of derelict ships. These derelict ships were probably left there during the civil war between humanity or when the AIs began the war of extermination. Additionally, the highest number of metal deposits are found in the human homeworlds, which the AIs have yet to build a presence in and clear out/recycle the junk ships. You, and all other human players, are salvaging the burned-out husks of humanity's fleets to fuel your own war effort against the AIs.