For when the Military Arc is Completed: Your Civilization orders you to send X Champions, Y Soldiers and Z conscripts for a war or something, and can be negotiated with a Recruiter. Also, volunteers can prepare by taking a weapon/shield and some food and signing up as a volunteer, and counting for the conscript quota. You can also refuse to send and threaten to break away.
If you do send soldiers and the war breaks out, there is a chance of a seige, and there is also a chance that a friendly army with your own squad in it to help you defeat said seige.
For when the Caravan Arc is completed: You can build wagons and send your own caravans, and deal at THEIR depot instead of your own once they arrive. Caravans have a chance to become missing so send soldiers to guard them! A wagon full of tribute to the mountainhomes might also bring lots of skilled migrants, lax taxes, or a complement of the Royal Guard to scope out your fort before the Royals themselves arrive.
For Integration of Adventurers: Night Creatures can form in fortress mode and form a colony nearby. Adventurers might come to try to kill said Night Creatures. I don't know if this is there but I've never seen night creatures at my fort before.
Adventurers might also come, stay at your dining room/inn if you let them in, and rest. They can either be friendly and perhaps pay for the food after they leave by leaving coins/loot or be hostile, and attempt to steal your Artifact Adamatine Axe so they can use it. Also, if any FB or Megabeast is found, they will cancel all stuff, gather their equipment, and attempt to fight the FB or Megabeast. Sometimes, they gain reknown at your fortress and a legend tag "Adventurer The Slayer of the Broodlings has gained reknown at Knifeslaughtered by killing the Forgotten Beast Deathhelmets." and influencing engravings.
For Traders themselves: They can sometimes arrive wounded by bandits and need to rest before trading, and are sometimes followed by an ambush squad of said bandits. This just means that the ambushers who follow caravans struck before arriving at your fort, but the traders managed to get away their first strike. This also means they might have lost the Liaison or head trader, wagons or pack animals, guards, and various goods. Finally, you can attempt to clear the road after the Military Arc by sending your squad of troops to flush the bandits out of the trade route. Not sure if it should be this complicated or if we should stay with ambushers strike caravans on map.
For other Civilizations: Sometimes they send their own settling party of elves/humans/goblins/kobolds to try to settle the same area, most likely during the first year if they didn't hear of you. They will have more or less members depending on civ and you can attempt to integrate them as migrants, let them form their own fort in peace, negotiate them to leave by paying them off or any other !!FUN!! things.
In the same way, herds of X-men might migrate on or near map to establish a colony/breeding area, making for a constant source of fighting until you Military Arc sending troops to clear it out, or somehow negotiate with them.
For more 'Natural' events: Migrations like the Serengeti Wildebeast or Monarch Butterfly migration, or even just the Canadian Geese-style migrations might have a path through your fort. Get your population ready for trapping, hunting, butchering, tanning, zoo-making, leatherworking frenzy as a massive herd/flock of them travels across your map, trampling things along the way (and turning saplings into mush) and making easy targets. Other civs might send harvesters to bring their own kills, but they are usually nuetral and not hostile unless you steal their kill.
Pockets of reactive/poisonous gas might be stuck underground, maybe near coal veins or brimestone like real life. If you hit a flammable pocket and manage to make a spark (I don't know, mining flint with a steel pickaxe? dwarves smoking? the kitchen/furnace?) it goes boom cave-in style, at least until we design a better cave-in/explosion system.
Stlagmitse and staglites (lol fail spelling) are like the columns in the caverns except they don't reach all the way up/down, and some have ramps on them allowing dwarves to climb up for a better view/crossbow platform.
Not sure if fire imps are magical, magma clowns, hatched creatures or whatnot, but it might be possible to find a breeding cave filled with females/portal to the circus/eggs/young imps allowing you to trap them for breeding, gather eggs for hatching or cooking, or send a message to the clowns hiding in the portal.